physics phd qualifying exam book

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2022 Exam - Solutions: Part 1 , Part 2 , Part 3 , and Part 4

2021 Exam - Solutions: Part 1 , Part 2 , Part 3 , and Part 4

2019 Exam - Solutions:  Part 1 ,  Part 2 ,  Part 3 , and  Part 4

2018 Exam - Solutions:  Part 1 ,  Part 2 ,  Part 3 , and  Part 4

2017 Exam - Solutions:  Part 1  and  Part 2

2016 Exam - Solutions:  Part 1  and  Part 2

2015 Exam - Solutions:  Part 1  and  Part 2

2014 Exam - Solutions:  Part 1  and  Part 2

2013 Exam - Solutions:  Part 1  and  Part 2

2012 Exam - Solutions:  Part 1  and  Part 2

2011 Exam - Solutions:  Part 1  and  Part 2

2010 Exam - Solutions: Part 1 and Part 2

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This volume is a comprehensive compilation of carefully selected questions at the PhD qualifying exam level, including many actual questions from Columbia University, University of Chicago, MIT, State University of New York at Buffalo, Princeton University, University of Wisconsin and the University of California at Berkeley over a twenty-year period. Topics covered in this book include the basic principles of quantum phenomena, particles in potentials, motion in electromagnetic fields, perturbation theory and scattering theory, among many others.

This latest edition has been updated with more problems and solutions and the original problems have also been modernized, excluding outdated questions and emphasizing those that rely on calculations. The problems range from fundamental to advanced in a wide range of topics on quantum mechanics, easily enhancing the student's knowledge through workable exercises. Simple-to-solve problems play a useful role as a first check of the student's level of knowledge whereas difficult problems will challenge the student's capacity on finding the solutions.

• Basic Principles and One-Dimensional Motions
• Central Potentials
• Spin and Angular Momentum
• Motion in Electromagnetic Fields
• Perturbation Theory
• Scattering Theory & Quantum Transitions
• Many-Particle Systems
• Miscellaneous Topics
• Index to Problems
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College of Liberal Arts and Sciences

Phd qualifying exam, what is the qualifying examination heading link copy link.

All Ph.D. students must take and pass a written qualifying examination in order to advance to doctoral candidacy. The qualifying exam is at the level of advanced undergraduate courses and many resources are available to students to aid in preparing for the exams, including previous years’ exams.

Please note all students, regardless of their academic standing, are eligible to take the qualifying exam.

Get More Info Heading link Copy link

• Document icon UIC Graduate Student Handbook
• Document icon Dept. of Physics Graduate Handbook
• Edit icon Past exam questions and solutions

Examination schedule Heading link Copy link

Please note: heading link copy link, all exams will be held in sel 2294. note that sel doors will be locked during this week. sel building access will be added to your i-card when you register for the exams with james nell., additional background and preparation materials heading link copy link.

The following list of textbooks should give you an indication of the minimum level at which you should prepare yourself for the qualifying exam. Remember that qualifying problems are typically at the level of the more difficult homework problems of our 400-level courses offered at UIC. To be successful at the qualifying exam both a solid understanding of the material and analytical skills are necessary. The latter requires basic mathematics and practicing problem solving.

• Fowles, Analytical Mechanics
• Marion and Thornton, Classical Dynamics and Systems
• R. Becker, Introduction to Theoretical Mechanics

Electromagnetism

• Griffiths, Introduction to Electrodynamics
• Reitz, Milford and Christie, Foundations of Electromagnetic Theory

Quantum Mechanics

• Griffiths, Introduction to Quantum Mechanics
• Amit Goswami, Quantum Mechanics
• Stephen Gasiorowicz, Quantum Physics
• N. Zettili, Quantum Mechanics
• Liboff, Introductory Quantum Mechanics

Thermodynamics, Statistical Mechanics

• Adkins, Equilibrium Thermodynamics
• Daniel Schroeder, An Introduction to Thermal Physics
• Reif, Statistical Mechanics
• Kroemer and Kittel, Thermal Physics

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Home / academic-programs / Graduate / Grad Student Handbook / V. Qualifying Examinations

• V. Qualifying Examinations

Passing the written qualifying examination is a requirement for all PhD students. Students have up to three opportunities to pass the five sections of the written qualifying examination:

• Classical Mechanics
• Electricity & Magnetism
• Mathematical Methods of Physics
• Quantum Mechanics
• Statistical Mechanics

Each section is a three hour, closed-book written examination, with one sheet of information (formulae, equations, etc.) provided. Each test has three questions. Students are required to turn in solutions to only two of these. In order to pass a section, students need to score at least 12/20 points, where each question is worth a maximum of 10 points. It is not necessary for a student to retake any section which they complete successfully .   Students are required to take all unpassed sections of the exam each time the exam is offered or forfeit that attempt .

UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations for the Written Qualifying examinations, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to the Graduate Program Coordinator privately prior to the scheduled exams.  

We encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089 or by email at  [email protected] .

All students in the Ph.D. program must pass a qualifying examination consisting of five written tests in the areas of Mathematical Methods for Physics, Classical Mechanics, Quantum Mechanics, Statistical Mechanics, and Electricity and Magnetism. Students have a first opportunity to take these five tests at the beginning of their first year. Once a student passes an examination in any one of the five areas they do not need to take an exam in that area again. If necessary, each student has a second opportunity to pass the written tests at the beginning of the second year. Students with at most one or two failed tests have a third opportunity to pass their remaining tests at the beginning of the winter quarter of their second year. Students who fail any of the remaining tests at this third and last attempt, and students who have not passed three or more of the five written tests after two attempts can either transfer to the terminal MS program (the MS degree is automatically awarded to students who passed at least ⅘ sections, and it requires an additional written research thesis for those who only passed ⅗ sections), or appeal to the Graduate Committee to continue on the PhD route. In this latter case, the Graduate Committee considers whether there is evidence of likely success in the PhD program. The Committee evaluates and reviews the student’s progress towards candidacy, including performance in courses and progress in research, and recommends possible remedial coursework or an oral examination, or recommends that the student transfer to the terminal MS route.

Past exams may be viewed at the password-protected webpage  https://drive.google.com/drive /u/0/folders/0ANgS2p7Ld_yZUk9P VA  (login with your UCSC google account, or contact the grad advisor to request access) . Past exams provide general guidance regarding the level of difficulty and style of the questions, but are not meant to exhaustively indicate which material is tested at a given section.  

Textbooks covering material at the level of the examination include:

• Mechanics: Marion and Thornton, Classical Dynamics of Particles and Systems , (all chapters). This is an undergraduate level text, used in many universities in the junior year.
• Electricity and Magnetism: Jackson, Classical Electrodynamics , esp. chapters 1-9, 11-14 (in principle, anything in the text may be covered in the exam).
• Quantum Mechanics: Shankar, Quantum Mechanics , entire text. One might want to supplement this with some text with a more extensive treatment of topics such as scattering theory and perturbation theory, with more physical examples. Possible texts include those of Sakurai and Baym.
• Mathematical Methods of Physics: This is covered at an advanced undergraduate level. Suitable texts include those of Boas and of Arfken, in their entirety. This section tends to be somewhat unpredictable, but it is good to have a mastery of elementary differential equations and complex variables (particularly contour integration, and topics such as convergence of series, etc.). Topics like Laplace transforms, fourier analysis, and the like appear with some regularity. You won't be expected to remember long formulas about special functions, but you might be given information (e.g. recursion relations, integral representations) and be expected to manipulate it to derive results.
• Statistical Mechanics: Wannier, Statistical Mechanics , and Plischke and Bergersen, "Equilibrium Statistical Physics." This section is covered at the graduate level although many problems can be solved with an undergraduate level of understanding.

Some advice on preparation:

• Allow plenty of time. The summer prior to the exam, you should try to minimize other commitments (research, travel, etc.). Plenty means a great deal -- the equivalent of many weeks, full time.
• Don't expect that you will master material simply by reading. It is important to work problems, from small exercises, to textbook problems and past exams. All studying should be done with pen and paper in hand. Invent exercises: derive formulas in texts, apply them to familiar day to day problems, etc. It is a good idea to spend some of your time studying with your friends. This will give you feedback on problems, and is also fun and good for your morale.
• Try to take a positive view of this experience. This is the last time you will be encouraged to take a broad view of physics. It is an opportunity to fill in gaps in your knowledge, explore material you didn't learn well in the past, read books that you have always wanted to read (e.g. some students study the Feynman lectures while preparing).

Statistical Mechanics Written Qualifying Exam Syllabus 

Note that the list of topic is only meant to provide a broad indication of the material covered by the written qualifying exam. This is not the syllabus for course Physics 219!

Note that questions that build on simple extensions or applications of the topics listed below might also appear in the test. 

• The zeroth, first, and second law
• Carnot engines
• Equilibrium and thermodynamic potentials
• Stability conditions
• The third law
• Random variables
• Probability distributions
• Many random variables
• Sums of random variables and the central limit theorem
• Rules for large numbers
• Information, Entropy, and Estimation
• Liouville’s theorem
• The Boltzmann equation
• The microcanonical ensemble
• Finite -level systems (2 , 3 state systems )
• The ideal gas
• Mixing entropy and the Gibbs paradox
• The canonical ensemble
• The Gibbs canonical ensemble
• The grand canonical ensemble
• Fluctuations in ensembles and relation to susceptibilities
• Fermi and Bose Distributions
• Black-body radiation
• Hilbert space of identical particles
• Canonical formulation
• Grand canonical formulation
• Degenerate Fermi gas, Sommerfeld expansion
• Degenerate Bose gas, Bose condensation and Superfluid He 4
• The cumulant expansion
• The cluster expansion
• Second virial coefficient and van der Waals equation
• Breakdown of the van der Waals equation
• Mean-field theory, Phase transitions (1 st   and 2 nd   order),  Critical behavior, Exponents
• The Landau theory of 2 nd   order phase transitions
• Saddle point approximation and mean-field theory
• Discrete symmetry breaking and domain walls, Energy entropy arguments of Landau Lifshitz and Peierls domain wall entropy
• Exact solution of 1-d Ising model, Transfer matrix formulation
• Scattering and fluctuations
• Correlation functions and susceptibilities
• Fluctuation corrections to the saddle point

Relevant recommended textbooks for SM:

• Mehran Kardar, Statistical Physics of Particles
• Mehran Kardar, Statistical Physics of Fields
• Pathria, Statistical Mechanics
• Kittel and Kroemer, Thermal Physics
• Plischke and Bergersen, Equilibrium Statistical Physics
• Wannier, Statistical Mechanics
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Qualifying Exam

The Qualifying Exam is an important part of the process of admission to candidacy. The oral exam seeks to give the student an opportunity to exhibit a broad knowledge of physics and an in-depth understanding of a particular area of physics that is not the one of their thesis research. The student should exhibit command of the material, an ability to extract the essential elements of a relatively recent development in physics, and the capacity to present this material to an audience of general professionals in a way that demonstrates their expertise.  It is required that students schedule the exam for the Winter or Spring quarter of their second year. To learn more about the exam, please review the policy (below):

2023-2024 Qualifying Exam Policy

2023-2024 Qualifying Exam Topic Submission Form

2023-2024 Qualifying Exam Action Items

Qualifying Exam Previously Approved Topics

2023-2024 Qualifying Exam Evaluation Form

Qualifying Exam FAQs

How many basic physics questions will I be expected to answer?

Questions will generally be related to the topic presented, but they may stray far from the initial discussion, depending on the circumstances, as commonly happens in a good physics discussion. This may be the result of an unsatisfactory answer to a previous question or may simply arise from questions from a committee member.

What are the committee members looking for in my talk?

We are generally looking for a clear description of the paper's key result and the basic physics behind it. While the main emphasis is on the science, a clear and crisp exposition will generally help the candidate. Note that while most of the exam clearly relates to the topic of your choice, you will need to know enough to provide context and make connections with a broader  range of  physics.  The presentation should be lecture/expository style, at a level accessible to any physicist. So start at the advanced undergraduate level and develop the explanation as fully as you can in the time available. You may be asked questions, both during and after the exam, on both the particular result being presented and on related topics.  The questions may be at any level, but good responses to foundational-level questions are most important. On-your feet thinking is encouraged and reasonable discussion of specialist-level questions might be considered a stretch goal.

How closely can the selected topic be to our current research?

You should identify a research topic from a field of interest to you that is also close to the forefront of current research. However, the topic cannot be in the same broad area of research as your intended research work. To clarify this point, you are required to identify your area of research as one of the four areas in the table below and select your topic from one of the remaining three:

How long should my presentation be?

One should expect the exam to last roughly 90 minutes (try to reserve a 2-hour block with your committee). The candidate should plan to talk for 45 minutes, leaving the remaining time for questions from the committee and a closed session. 

Who is on the Examination Committee?

The examination committee for an oral exam will ordinarily consist of three faculty members. One of tthese will be chosen from the members of the Qual Exam Committee (QEC). Ordinarily, all three oral exam committee members will be faculty within the Physics Department, Applied Physics, or SLAC (PPA and Photon Science), but exceptions may occur for special reasons, as decided by the QEC. After approval, the student must contact the assigned committee and schedule the examination – this is often the most difficult part of the whole process, so ask your committee early (and often!).

Are there any examples of past topics that have been approved by the committee?

Please see this table of  APPROVED TOPICS  for examples of topics that have been approved.

Can I choose a topic similar to that chosen in prior years? What if two students in a given year choose the same topic?

There is no prohibition against a student choosing a topic that was covered in a previous year or that happens to have been chosen during the current year by another student but it is recommended that you do not pick a topic directly from the previously approved topics list. Students must work independently; i.e there should be no contact or collaboration in preparing for the exam with other grad students. One exception is that students may give practice presentations to other students, and seek presentation advice as a consequence of those practice runs.

I'm interested in topic X. Who can I talk to to ensure that this is acceptable for an exam?

We can't pre-judge exam topic proposals. Please take a look at the descriptive materials and make the best judgment that you can as to whether the topic is appropriate and sufficiently far from your PhD research area/style. Prepare and submit your proposal. If your proposal is evaluated as not meeting requirements, you will be given a chance to chose and prepare an alternate topic.

• Past Physics Ph.D. Qualifying Examinations
• Student Resources

The following are recent Ph.D. qualifying examination for physics graduate students. Exams are given twice per year (in August and January) over two days with a four-hour session each day. These are provided for Illinois Tech students to use in their preparation. All of the documents are in  Adobe Acrobat  Portable Document Format (PDF). 

Learn more...

Qualifying Examination

Recent qual exams.

The Department of Physics requires all Ph.D. candidates to pass a qualifying examination. Its purpose is to ensure that a student has sufficient general knowledge in physics to proceed successfully toward the Ph.D. degree.

The qualifying examination is a written examination administered in two evening sessions. Each session contains a problem on classical mechanics (including relativity), electricity and magnetism, quantum mechanics, and thermodynamics (statistical mechanics). The exam tests competence in material that will have been covered in a solid undergraduate degree course in physics, but with the depth of understanding and technical facility expected after one year's enrollment in a graduate program. Accordingly, the level is sometimes said to be intermediate between undergraduate and graduate. The material covered is as follows :

Classical mechanics at the intermediate level (Physics 326), plus the special theory of relativity. Typical texts are Marion, Symon, Becker, and Fowles .

Electricity and magnetism at the intermediate level (Physics 436), including boundary value problems. Typical texts are Lorrain, Corson and Lorrain, Reitz, Milford and Christy, and Nayfeh and Brussel , with mathematical competence expected at the level of Chapters 1 through 7 of Jackson , and the electromagnetism parts of Wyld . (Cables and waveguides may be covered on the exam, although not at the level of Chapter 8 in Jackson .)

Statistical physics at the intermediate level (Physics 427), including the use of the Boltzmann, Gibbs, Fermi-Dirac, and Bose-Einstein distributions, classical and ideal gases, and black-body radiation. Typical texts are Chapters 1 through 14 of Kittel and Kroemer and Chapters 1 through 13 of Reif . These ranges of chapters are suggested as a study guide; other topics may be covered on the exam, as shown in the example problems .

Quantum mechanics at the intermediate level (Physics 486,487) and the beginning graduate level (Physics 580). Typical graduate texts are Dicke and Witte, Gasiorowicz, Park, Merzbacher, Baym, Landau and Lifshitz, Sakurai, and Schiff . Typical undergraduate texts are Eisberg, Park, and Cassels .

The examination is constructed to test your knowledge of the fundamental principles in each subject, applied to situations of physical interest. Elaborate formal questions are avoided. In particular, the portion of the examination dealing with quantum mechanics covers simple applications of Schroedinger wave mechanics to both bound-state and scattering problems, few-level systems, the Pauli theory of electron spin, and perturbation theory.

Admitted graduates are strongly encouraged to prepare for the qualifying examination by working through past exams. These exams, which give the best indication of style and content, are available on-line . More information is available in the Qual FAQ . You may also find the Physics Formulary or the NIST " Reference on Constants, Units, and Uncertainty " helpful.

When the Qual Exam is Offered

The written qualifying examination is given during the first or second week of the fall semester. Students entering the Ph.D program are required to take the qual by the beginning of their third semester that they are enrolled in the department, although they may elect to take it earlier. In the event of failure on the first try, a student is allowed one further attempt, which must be taken at the next offering. A "free shot" is available to all students at the time of their first enrollment. Failure on the free shot is not recorded and does not count against the student, but a pass is a bona fide pass. Thus, if you do some preparation, we encourage you to take the free shot; you have nothing to lose, and you may gain valuable insight into your own strengths and weaknesses to guide you in your selection of classes.

Some notes are allowed during the qual. You may bring one "pure math" integral table (e.g. CRC Handbook of Mathematical Formulae , or Gradshteyn and Ryzhik's Tables of Integrals, Series, and Products ). You may not bring handbooks or textbooks containing physics formulae. Electronic calculators or slide rules may be used, but no other books, handwritten notes, laptop computers, or other aids are permitted in the examination room. A printed handout of traditional physics formulae will be supplied with the exam. In recent years, the overall pass rate on the qualifying examinations has been 80-90 percent.

For more information about the qual and relevant dates, contact the Associate Head for Graduate Programs (227 Loomis, 217-333-3645).

Frequently Asked Questions (FAQ)

Qual On-line Archive

Graduate Admissions Contact

Lance Cooper Associate Head for Graduate Programs 227 Loomis Laboratory (217) 333-3645 [email protected]

Have questions about the admission process? Read through the Admissions pages or contact us.

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Qualifying Exam Requirement

Old-style qualifier.

The next Qualifier will be held on: August 14 & 15, 2024 .

New Qualifier Requirement

Students enrolling in the Ph.D. degree beginning in the Fall term of 2021 will be required to satisfy the new Qualifier Examination requirement, which consists of two parts:  Part A corresponds to the material in the Fall semester of the core graduate course sequence (PHYS 610 and PHYS 612) while Part B corresponds to the material in the Spring semester (PHYS 611 and PHYS 613). The requirement is that students satisfy both parts.

Each part of the requirement can be completed in one of two ways:

• Pass a section of the exam when it is given.

                                       —OR—

• Courses taken at other institutions cannot be used to substitute for courses in these sequences.

Students enrolled prior to the Fall term of 2021 may either satisfy this new requirement, the requirement in place prior to this or be deemed to pass via a hybrid procedure discussed in the Transition Period section below.

Here are some previous exams:

Timing and the Qualifier Clock

The Qualifying Examination will be offered once per year prior to the beginning of each semester.  Part A will be given prior to Fall semester and Part B prior to Spring semester.

Under ordinary circumstances, students will be permitted up to 4 (continuous) semesters to satisfy this requirement once the `’Qualifier Clock’’ has started.  The Qualifier Clock may be paused at the discretion of the Director of Graduate Studies at a student’s request, but only under exceptional circumstances. Such circumstances may include medical issues, mental health issues, the need to care for a family member or some unexpected change in situation that significantly affects the student’s ability to study.

The system is designed so that most students should be able to satisfy the requirement within two semesters; the additional two semesters are permitted to allow students additional opportunities to satisfy the requirements, if needed.

The Qualifier Clock begins when

• A student attempts either section of the Qualifying Exam

A student has begun to take at least one class in the PHYS 610-611 sequence and at least one class in the PHYS 612-613 sequence. 

Some examples:

• A student who enters the program with a Master’s Degree in physics, or more generally a student who has taken and done well in a substantial number of graduate-level physics courses prior to joining the program could choose to take the Part A of the Qualifying Examination prior to their first semester. Such students would have until the end of the Spring semester of their second year to satisfy the requirement, unless the Qualifier Clock is stopped for an exceptional reason. 
• A student who enters the program with a strong well-rounded preparation in undergraduate Physics but limited or no experience with graduate-level courses would normally be expected to take PHYS 610 and PHYS 612 in their first semester and thus would have their Qualifier Clock begin at the beginning of their first Fall semester.  Such students would have until the end of the Spring semester of their second year to satisfy the requirement, unless the Qualifier Clock is stopped for an exceptional reason.
• A student who enters the program with some gaps in their undergraduate preparation would find it prudent to close these gaps by taking some undergraduate classes in their first year and postpone taking one or both of the sequences of core graduate-level classes until their second year.  Such students would have until the end of the Spring semester of their third year to satisfy the requirement unless the Qualifier Clock is stopped for an exceptional reason.
• A maximum of two attempts at Part A of the Qualifier
• A maximum of two attempts at Part B of the Qualifier
• A maximum of two attempts to receive a grade of B or better for each of the core graduate-level classes; if a student begins taking one of these classes and withdraws from it after the drop/add period, it will count as an attempt unless there are substantial extenuating circumstances.

Recommended Paths to Satisfy the Requirement

While students are permitted to take the exams whenever they are offered, it is a strong recommendation by the Department that:

• Students who have already taken the core courses and did not achieve a grade of B or better in at least one, are encouraged to restudy the material in that course and take the appropriate section or sections of the Qualifying Exam.
• Students who enter the program having taken and done well in a substantial number of graduate-level physics courses (for example students with a Master’s Degree) should consider satisfying the requirement via the examination.
• Students who did extremely well in PHYS 610 and PHYS612 (grades of A in both) and who found the material to be largely straightforward may consider taking Part B of the exam.

In particular:

• Students who enter the program without having taken and done well in a substantial number of graduate-level physics (for example students with a Master’s Degree) should not attempt Part A of the exam prior to their first semester. Such students will be well served by taking the recommended core classes.
• Students who enter the program without having taken a substantial number of graduate-level physics (for example students with a Master’s Degree) should in general not attempt Part B of the exam prior to their second semester. The exception to this recommendation is for students who did extremely well in PHYS 610 and 612 (grades of A in both) and who found the material to be largely straightforward and redundant with their prior knowledge.
• A student who enters the program with some gaps in their undergraduate preparation should postpone starting the Qualifier Clock and take some undergraduate classes in their first year and postpone taking one or both of the sequences of core graduate-level classes until their second year.

Criterion for passing the exam

There is no fixed score for passing the sections Qualifying Exam.  In marginal cases, whether a student passes a given exam with a given score dependson:

• An assessment of the overall difficulty of the exam.
• The performance on the exam in the context of a student’s overall academic record.

Consider, for example, a student with an overall marginal score who would have been clearly passed had they not done poorly on one question dealing with quantum mechanics.  If that student had done well in graduate-level quantum mechanics classes prior to the exam, the student would likely be passed.  On the other hand, if that student had never taken a graduate level-class the student would likely not be passed.

Structure of the exam

Each part of the exam lasts four hours and consists of 4 questions, each of which may have multiple parts.  Students will be graded on all four questions. 

During the transition period, the style of the exam questions will likely be similar to our old qualifying exam, since some of the same questions may appear on both the new and old exams . As things progress it is expected that the new exam questions will more closely follow what is done in the core graduate classes.

Transition Period

As we change over to the new system, there will be students who enrolled prior to Fall 2021 in the program.  These students can satisfy the requirement in one of three ways:

• Students can satisfy the old Qualifier requirement by passing both Part I (classical physics) and Part II (quantum physics).
• Students can satisfy the new Qualifier requirement.
• Students can satisfy a hybrid of the two with possible accommodations made due to the mismatch of the old and new Qualifier and old and new courses; the particular form that such a hybrid will take place depends on a student’s particular circumstances and needs to be approved by the Director of Graduate Studies.

In accommodating students who wish to pass via a hybrid of the requirements  the general principle of the new requirement that enables students to satisfy the requirement by explicit exams or courses will be used.  The following situations will generically be deemed as satisfying the requirement:

• A student who has passed with a B or better at least four of the following courses 601, 604, 606, 622 and 623.
• A student who has passed Part I (classical) of the old-style Qualifier and also passed with a B or better at least two of the following courses 604, 622 and 623.
• A student who has passed Part II (quantum) of the old-style Qualifier and also passed with a B or better at least two of the following courses 601, 604 and 606.

Students enrolled prior to Fall 2021 who have partially fulfilled the hybrid requirements may be unable to complete them in a straightforward way since the course offerings and exam structures have changed.  In such situations 

• In some cases, a student may be able to complete the requirement by taking the old-style Qual. (This option is viable for students who have either passed one part of the old-style Qual or have passed with a grade of B or better a number of our old-style core course.)
• In cases where none of the hybrid paths discussed above are viable, a student should arrange with the Director of Graduate for some alternative method of completing the requirements. This might include taking and passing one or more of the new-style courses, taking one of the new-style exams, or if agreeable to the student taking and passing an oral exam. The exact method agreed to will depend on the student’s particular academic circumstances.

The Qualifying Exam consists of two parts: Classical Physics and Quantum Physics.

First-year students are welcome to take a “free try” during January of their first year. (Especially well-prepared students can request permission to take their free try in August when they first arrive.) This will not count toward the three exam limit.

A year after matriculation, students must take the “first try” of the exam, and take their second and third tries in the subsequent semesters. If the student cannot pass both parts of the Qualifying Exam after the Fall of their third year, they can appeal the Qualifying Committee to have an Oral Examination.

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PhD Handbook

The Ph.D. is at its core a research degree. The degree requires substantial original research, presented in the form of a dissertation. The path to the Ph.D. consists of two stages. In the first (pre-dissertator) stage, the student passes the department’s Qualifying Examination, completes required coursework (core and minor), and starts research with their faculty research advisor in preparation for the Preliminary Examination. Once the student completes all departmental and Graduate School requirements and passes the Preliminary Examination, the student has achieved dissertator status. In this stage of the program, the student focuses on their thesis research and completes their dissertation. The student defends the dissertation in the thesis defense. The student then deposits the dissertation with the Graduate School, which is the final step to the degree. The requirements for the Ph.D. are in accordance with the department’s learning goals of the program, and UW-Madison Graduate School policy. The full details of the program requirements can be found in the GUIDE .

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CREDIT REQUIREMENTS

Total Credits

The Physics Ph.D. degree includes a number of coursework and credit requirements. The Ph.D. degree itself requires 51 credits in total to align with the Graduate School minimum graduate degree credit requirement:

https://grad.wisc.edu/documents/minimum-graduate-degree-credit-requirement/

Credits Before Dissertator Status

The Graduate School minimum graduate residence requirement requires that at least 32 credits towards the doctoral degree must be completed prior to achieving dissertator status:

https://grad.wisc.edu/documents/minimum-graduate-residence-credit-requirement/

The 32 credits are achieved via the core coursework sequence, the Ph.D. minor, and a combination of other coursework and Physics 990 research. 15 of the credits will be accumulated from the Physics core coursework and a minimum of 9 credits will be accumulated from the minor. The remaining 8 credits can include research or other coursework.

Graduate Level Credits

The Graduate School minimum graduate coursework (50%) requirement states that at least 50% of the 51 credits must be at least 700 and above or courses with the Graduate Coursework (G50%) attribute:

https://grad.wisc.edu/documents/minimum-grad-coursework-requirement/

To determine which courses can be used to satisfy the graduate level (G50%) credit requirement, please consult http://enroll.wisc.edu   (Search: “Other Options”, check the box “50% Graduate Coursework Requirement”). This will provide accurate results of which courses have been approved through the University to count towards the G50% requirement.

STEPS TO THE PHD

The steps to the Ph.D. are:

• Pass the departmental Qualifying Examination
• Complete the required core coursework
• Complete the minor requirement
• Acquire a faculty research advisor and begin research
• Pass the Preliminary Examination
• Complete thesis research and defend the dissertation
• Deposit the dissertation with the Graduate School

SATISFACTORY PROGRESS

• Enroll each semester according to the Graduate School minimum enrollment requirements ( https://policy.wisc.edu/library/UW-1208 ) and the department’s enrollment requirements (described below).
• Maintain an overall graduate GPA of 3.0 or above (Graduate School requirement: https://policy.wisc.edu/library/UW-1203 ).
• Pass each of the four sections of the Qualifying Exam at the Ph.D. level (nominally 60% or above) within the four officially allowed consecutive attempts (see Qualifying Exam section below), as required for continuation in the Ph.D. program.
• Make progress on completing relevant coursework in a timely fashion.    This includes core coursework, minor coursework, and satisfying Graduate School credit requirements (further details are described below under coursework and minor requirements).
• Make progress in acquiring a faculty research advisor and joining a research group in a timely fashion, preferably by the beginning of the summer following the first year in the program.
• Make satisfactory progress in research as judged by the faculty advisor.
• A typical timeline is for students to take and pass the Preliminary Exam is in the third year of the Ph.D. program, though this can vary significantly by subfield.  
• Make satisfactory progress in research as judged by the faculty advisor by earning a P (Progress) or S (Satisfactory) in 990 research each semester.
• Successfully completing and defending the doctoral thesis within five years of passing the Preliminary Exam.

FIRST-YEAR COMMITTEE

A committee of 4-6 faculty serve, in pairs, in the capacity as advisors for 1 st year grad students. The purpose of the committee is to provide consistent guidance on 1 st year courses, student specific qualifying exam guidance, and to provide mentorship before students establish a long-term thesis advisor.

Each incoming student will be scheduled for a meeting with their assigned First Year Committee faculty pair in advance of the fall semester.  Committee members will meet again with students before the start of the second semester and at the end of the second semester to check on progress and advise students on future course work, qualifying exam progress, and guidance finding a permanent thesis advisor.

The Graduate School policy indicates the minimum enrollment requirements each semester:  https://grad.wisc.edu/documents/enrollment-requirements/

Physics Ph.D. students must enroll in at least 2 credits of Physics coursework each semester until the Preliminary Exam is completed. Individual 1 credit courses or a combination of 1 credit courses, such as Physics 701 and 801, do not count towards this requirement.

It is often suggested that students who hold teaching assistant (TA) appointments take only 6 credits during their first semester, as more than this may affect performance in both teaching and coursework as students become acquainted with the demands of the program. After the first semester, students are encouraged to take three courses per semester until they reach dissertator status. All students are encouraged to consult with the faculty advisor and mentoring committee to discuss the course schedule each semester.

Core Course Sequence

All physics Ph.D. students must take the Physics core course sequence and achieve a grade of B or better in each core course or repeat these courses until a B grade is achieved.  The core courses are as follows:

• Physics 711 (Dynamics)
• Physics 715 (Statistical Mechanics)
• Physics 721 (Electrodynamics)
• Physics 731 (Quantum Mechanics)
• Physics 732 (Quantum Mechanics)

Course Waivers: Prior Coursework

Students who believe that they have done graduate-level work in one or more of the core course subjects prior to their arrival may be eligible for course waivers, or they may decide to try to test out of these subjects. Course waivers or test-out forms are available for those students who have taken equivalent courses at another institution. Waivers of core courses can be granted for credits earned at other universities in equivalent graduate-level courses, pending approval by the Associate Chair for Graduate Studies. Students who believe that they qualify for a waiver of the course requirement for a core course based on prior graduate course work from another institution should request consideration for a waiver within the first month of the graduate program. The Graduate School will allow these credits to count towards the graduate degree at UW-Madison only if they were earned post-baccalaureate as outlined in the Prior Coursework policy:

https://grad.wisc.edu/documents/prior-coursework/

Students who believe that they have had graduate level coursework in a subject or subjects comparable to what is covered in the core courses, but who do not clearly qualify for a waiver of any specific courses, have the option of trying to test out of the course. At a minimum, this typically requires passing the final exam for the course at a level that would clearly lead to a grade of B or better in the course. Requests to test out of core courses should be made to the Associate Chair for Graduate Studies during the first month in the graduate program. Testing is to be completed during the first semester in the graduate program. Testing out of a course does not include any credits towards a graduate degree at UW-Madison.

Breadth is a required component of graduate study at UW-Madison.  The Graduate School policy outlines the minimum requirements for all doctoral minors:

https://grad.wisc.edu/documents/minors/

The purpose of the minor is to add breadth to the Ph.D. course of study by broadening students’ knowledge of physics or related fields, and/or to support their research and prospective professional activities. There are two options for completing the minor – Option A: External or Option B: Distributed. Minors must be approved by the faculty advisor and the Associate Chair for Graduate Program.  Option A: External minors must also be approved by the appropriate channels in the external department. The Ph.D. Minor Form must be completed, signed, and returned to the Graduate Coordinator at or before the time the warrant for the Preliminary Exam is requested.  In addition, all Graduate School students must utilize the Graduate Student Portal ( MyGradPortal in MyUW) to  add/change their doctoral minor.  (NOTE:  Physics students will not be allowed to select a Physics GMIN.  If you are completing a Distributed minor (see below), you should select Distributed GMIN.)

Option A Minor: External

• Minimum of 9 credits in an external department at the graduate level
• Consists of coursework in one single department outside of the Department of Physics and is named accordingly
• Consult with the minor department for specific minor requirements and the processes to declare an external minor in another department
• A list of all external doctoral minors and the Graduate School external minor requirement: https://guide.wisc.edu/graduate/#doctoralminorstext

Option B Minor: Distributed

• Minimum of 9 credits of minor coursework taken in one or more departments
• Must include a minimum of 3 credits in Physics at or above the 500 level
• Coursework must be outside of the student’s area of specialization, form a coherent theme, and provide breadth in programmatic or professional development
• Physics core coursework may NOT be counted towards the minor
• Additional coursework relevant to the student’s area of specialization may NOT be counted towards the minor
• Up to 3 credits of the 9 credits may be satisfied by Physics 900 (Colloquium) which is a 1 credit course offered every semester
• 1 credit of the 9 credits may be satisfied by Physics 701 (First Year Seminar)

Physics Minor for Non-Physics Students

The doctoral minor requirement in Physics for non-physics graduate students is 9 credits numbered above 300, each passed with a B or better. The program must be approved by the Associate Chair for Graduate Studies before it is completed:

https://guide.wisc.edu/graduate/physics/physics-doctoral-minor/index.html

The Graduate School provides information on graduate assistantships, benefits, minimum stipend levels, and stipend levels by program: https://grad.wisc.edu/funding/graduate-assistantships/

The Graduate Assistantship Policies and Procedures (GAPP) document outlines campus level policies and procedures for Project (PA), Teaching (TA), and Research (RA) Assistants.   https://hr.wisc.edu/policies/gapp/

Teaching Assistant (TA)

Many Physics Ph.D. students will hold a teaching assistantship (TA) at some point during the program. A TA is both a job and a means of financial support for graduate study. Because of the coexistence of these two functions, the relationship between the department and the individual teaching assistant (TA) is complex. The advantages of holding a teaching assistantship for at least one semester during graduate studies are that teaching activities solidify and deepen the teaching assistant’s undergraduate education in physics, help improve communication skills, and help prepare for a possible career in teaching. Because teaching is a job, the Department of Physics conducts regular TA evaluations. TA’s are evaluated by their students at the middle and end of each semester.  The purpose of the mid-term evaluation is for the TA to get feedback from the students (who remain anonymous), while there is still time to change teaching practices. The mid-term evaluations are not part of the TA’s permanent record. The final evaluation results in a letter, which does remain on the TA’s record, in which the TA’s performance is classified as either Excellent, Very Good, Good, Satisfactory, Marginally Satisfactory, or Unsatisfactory.

Because teaching is a means of financial support for graduate study, the Department of Physics typically admits graduate students with a guarantee of support in the form of a TA. This guarantee is described in each student’s offer of admission. During the time covered by the funding guarantee, students who are not supported as RA’s or Fellows, and who remain in good standing and making satisfactory progress, are guaranteed by the department to be supported as TA’s during the academic year.

After the natural expiration of the funding guarantee, students who need TA positions during the academic year may apply for them, but cannot be assured of receiving them. The number of TA positions available depends on the number of undergraduates who enroll in physics classes that use TA’s, as well on the percentage time of each position. Whereas guarantees of support typically specify 50%-time appointments, the minimum percentage required for a TA to receive a tuition remission is 33%. The Department of Physics sometimes offers non-guaranteed graduate students 33% positions, in order to maximize the number of students who might receive the tuition remission. On occasion students have requested 33% positions rather that 50% positions in order to free up more time for research. If a TA in the Physics Ph.D. program switches to another graduate program on campus, the physics department’s commitment to continuing support is terminated.

There are a small number of TA positions available in the summer term. Please note that the support guarantee does not extend into the summer. Depending on the number of requests, TA positions may or may not be available for all who request them. For further information about summer TA positions, please consult the Director of Undergraduate Studies. The majority of TA positions are in large general Physics classes for non-physics-majors. TA’s in these classes lead both discussion sections and laboratory sections. There are also a few TA positions in smaller, more advanced classes for physics majors. These are usually (although not always) given to experienced TA’s. Some involve discussion only (no lab), others involve lab only (no discussion).

Research Assistant (RA)

Many Physics Ph.D. students will hold a research assistantship (RA) at some point during the program.  RA positions are made available by individual professors to students who have decided on their field of research. Students who wish to be considered for an RA appointment should contact the faculty directly.

Fellowship opportunities for graduate students include external fellowships, as well as supplemental fellowship opportunities that are available through the UW-Madison campus or the Department of Physics. UW campus fellowship opportunities include University Fellowships and Advanced Opportunity Fellowships (AOF), which are awarded by the Graduate School upon recommendation of the Department of Physics during the admissions process. The Department may also have fellowships available for incoming first-year graduate students.  Funding for graduate student fellowship support is made possible by generous endowments from Physics Department alumni. Information about fellowships.

QUALIFYING EXAM

The qualifying exam requirement is designed to verify that any student leaving UW-Madison with a Ph.D. in physics has a sophisticated understanding of undergraduate physics. Undergraduate physics is a body of knowledge that is critical to experimentalists and theorists.

The qualifying exam is a written exam that assesses students’ understanding of core physics topics at the undergraduate level. The exam helps to ensure the strong foundation that is needed for demonstrating mastery of core physical concepts in Classical Mechanics, Electricity and Magnetism, Quantum Mechanics, and Statistical Mechanics, which is one of the learning outcomes for the physics Ph.D. program. https://guide.wisc.edu/graduate/physics/physics-phd/#learningoutcomestext

The exam is offered twice a year. The dates will be posted on the Graduate Program Events calendar:  https://www.physics.wisc.edu/twap/?name=grad     Students with special requirements must consult with the Graduate Coordinator in advance (at minimum two weeks before the exam, or earlier if a specified deadline is given).

The exam is separated into four sections:

• Classical Mechanics (CM)
• Electricity and Magnetism (EM)
• Statistical Mechanics/Thermodynamics (SM)
• Quantum Mechanics (QM)

The nominal Ph.D. passing score for each section is 60% and the nominal Master’s passing score for each section is 50%.

Each exam section can be passed independently. If a student receives a failing score on one or more sections of the exam, in subsequent attempts the student only needs to take the section or sections of the exam that remain to be passed.

All physics Ph.D. students have four consecutive opportunities within the first two years of the program to pass the exam in its entirety at the Ph.D. level. All entering Ph.D. students are required to take the qualifying exam in its entirety in their first semester in the program.

Due to the COVID-19 pandemic, the timeline for students who started the program in Fall 2020 to complete the qualifying exam requirement with the four allowed attempts is extended by one semester (Fall 2022).

Students that pass all sections of the exam at the Ph.D. level within the four allowed attempts have passed the department’s qualifying exam requirement and have received qualification status for continuing in the Ph.D. program.

Exam Structure

The qualifying exam is held at the start of every fall and spring semester. Each section of the exam is 1.5 hours long. .

Each section of the exam consists of five problems. Students are to do the first two problems, which are at the calculus-based introductory level, and to do two other problems (out of three offered) at the intermediate/advanced level. Students must only submit answers to these four problems for each section of the exam. The first two problems comprise one-third of the total score, and the second two chosen problems comprise the remaining two-thirds of the total score.

Exam Topics

The exam covers standard topics as included in undergraduate physics courses in CM, EM, QM, and SM at both the introductory and intermediate/advanced levels. These topics may include:

• CM: motion in electromagnetic and gravitational fields, rigid bodies, coupled oscillations, and continuum vibrations;
• EM: statics, fields in matter, time-dependent fields, Maxwell’s equations, light and radiation (with optics and circuits covered at the introductory level);
• QM: wave mechanics, matrix mechanics, observables and measurements, angular momentum, perturbation theory, elementary atomic physics, and elementary scattering theory;
• SM: thermodynamics and statistical mechanics of matter and radiation.

Grading Policies

The exam is graded anonymously by faculty.  The Qualifying Exam Committee reviews all graded problems in detail. It is only after this thorough review that the final grade of pass or fail for each student in each exam section is assigned. The results are then unblinded and distributed.  Students receive their scores and the grading rubrics used by faculty in grading the exam.

Students may request a review of their grades for specific exam problems to the chair of the Qualifying Exam Committee at any point within two weeks after the exam is returned.  The committee chair consults with the faculty that graded the problems in question and returns the final grade determination to the student.  Students should be aware that the grading rubrics used for assigning partial credit, which are also reviewed prior to the final pass or fail score assignments, are generally respected unless there are obvious inconsistencies or errors.

Appeal Process

If a student does not pass all four topical areas of the written qualifying exam at the Ph.D. level after the four exam attempts, the student can request an appeal. An appeals committee is then formed to assess the student’s case. The appeals committee consists of a faculty member of the student’s choosing, such as the student’s faculty advisor, and two other faculty that are to be determined on a case-by-case basis by the Qualifying Exam Committee. Further information about the appeals process will be provide on an individual basis when relevant at the time when qualifying exam scores are returned.

The appeal is designed to be a broad assessment that includes the student’s prior qualifying exam results, performance in graduate courses, and progress to date in research. Upon evaluating all factors, the appeals committee makes the final decision as to whether the student has achieved qualification status to continue in the Ph.D. program.

FACULTY RESEARCH ADVISOR

The responsibility to acquire and be accepted by a faculty research advisor, is entirely with the student. Acceptance for Ph.D. research by a faculty member depends on the professor’s appraisal of the student’s potential for research and on the ability of the professor to accept a student at that time. All incoming students are assigned a temporary advisor to help oversee their progress in the first few semesters in the program, but the temporary advisor is not automatically the research advisor unless there is a clear and concrete understanding between both the student and the faculty advisor that the student has already been accepted by that professor into their group.

To aid incoming students in selecting a research area and faculty advisor, Physics 701: Introductory Seminar, is offered each fall semester.  In this course, professors from each of the research groups describe their research, show their laboratories, and discuss matters of general interest to graduate students. First-year students are required to enroll in Physics 701.

Graduate students should begin research work as early as possible. Ideally students make progress in acquiring a faculty research advisor and joining a research group in a timely fashion, preferably by the beginning of the summer after the first year.  The summer after the first year is the ideal time to do research unencumbered by course work or teaching. It is also very important to determine summer funding support options as soon as possible. Ideally most students will have begun a trial project with an advisor or at least made the necessary introductions and have at least one solid prospect by the end of the first year.

MASTER’S DEGREES

Master of Arts (M.A.)

The master of arts degree is a purely academic degree, requiring 30 credits of graduate course work, completion of the core graduate coursework and passage of the qualifying exam at the master’s level. It is designed to strengthen the student’s physics background and enhance the opportunities for employment as a physicist or in physics education.

To earn the M.A. degree in the Department of Physics, a student must satisfy the department’s minimum graduate-level credit requirement and pass the qualifying exam at the master’s level. The department requires at least 30 credits at the 500 level or above. 15 of the 30 credits must be earned from taking the physics core graduate courses, each passed with a grade of B or better. These courses are Physics 711 (Dynamics), 715 (Statistical Mechanics), 721 (Electrodynamics), and 731 and 732 (Quantum Mechanics). The remaining 15 credits may be earned through a combination of coursework, directed study, and research to be determined in consultation with the student’s faculty advisor. The courses should be selected in consultation with the student’s faculty advisor to best meet the student’s professional objectives.

The M.A. degree requires the student to complete the add/change program/plan process through the Graduate School. In this case, the student must request to “add” the M.A. plan to their student record. Once the M.A. plan has been added to the student record, and all M.A. degree requirements have been met, a warrant request can be made to the Graduate Coordinator, allowing at least three weeks for the warrant to be processed.

Master of Science (M.S.)

The master of science degree in Physics requires the completion of a directed master’s project and thesis in the student’s area of interest, completion of the core graduate coursework, and passage of the qualifying exam at the master’s level. It is designed to strengthen the student’s background and experience in physics, and enhance the opportunities for employment as a physicist or in physics education.

To earn the M.S. degree in the Department of Physics, a student must satisfy the department’s minimum graduate level credit requirement and pass the Qualifying Exam at the Master’s level. The department requires at least 30 credits at the 500 level or above. 15 of the 30 credits must be earned from taking the core graduate courses, each passed with a grade of B or better. These courses are Physics 711 (Dynamics), 715 (Statistical Mechanics), 721 (Electrodynamics), and 731 and 732 (Quantum Mechanics). The remaining 15 credits may be earned through a combination of coursework, directed study, and research to be determined in consultation with the student’s academic advisor. The courses should be selected in consultation with the student’s advisor to best meet the student’s professional objectives.

Additionally, the student must present satisfactory evidence of scientific research, writing, and presentation skills. This will usually be done through a master’s research project that results in the submission of a master’s thesis written at a satisfactorily professional level, together with an oral presentation of the project in a master’s thesis defense.

The M.S. degree requires the student to complete the add/change program/plan process through the Graduate School. In this case, the student must request to “add” the M.S. plan to their student record. Once the M.S. plan has been added to the student record, a warrant request can be made to the Graduate Coordinator, allowing at least three weeks for the warrant to be processed.

PRELIMINARY EXAM

The Preliminary Exam must be passed for admission to candidacy for the Ph.D. and to achieve dissertator status through the Graduate School. It should be taken no later than the end of the fifth semester in the program, unless a student has received approval for an extension.  If the Preliminary Exam not passed on the first attempt, it may be repeated once before the end of the sixth semester.

The Preliminary Exam is intended to test whether the student has mastered the physics and technology necessary for research in the proposed general area of study, and to assess whether the student is on track to satisfying the department’s learning goals for the Ph.D. degree. The Preliminary Exam is held before the student’s Preliminary Exam Committee, which typically consists of four members:

• Faculty research advisor, who serves as the chair of the committee
• Faculty representative from the departmental Preliminary Exam Committee (student should contact the current Prelim Committee Chair to obtain this member)
• Two additional committee member(s) typically chosen by the student in consultation with their advisor.  Typically a UW-Madison faculty either in physics or another related department.

The exam is typically scheduled during a two-hour time block.  The student gives a presentation aimed at a general physics audience and should be understandable for a physicist working in an entirely different area.  The format can vary slightly depending on the research advisor and research group, but it typically begins with a one-hour presentation covering a subject in the student’s chosen area of research, and is followed by a question and answer period designed to assess the student’s background knowledge and research potential. The committee will ask questions to clarify points made in the talk and determine if the student adequately understands the physics behind the topics that were discussed.  The question and answer period typically takes place both in open session (in front of a general audience) and in closed session (just in front of the committee). The committee will deliberate the exam outcome in closed session, and communicates the result to the student once the decision is made. The committee will indicate the result of pass by signing the Preliminary Exam warrant.

A student planning to take the Preliminary Examination will need to present a completed and signed Minor Form and request a Preliminary Examination warrant from the Graduate Coordinator at least three weeks prior to the date of the examination. After the exam, the Graduate Coordinator will route the warrant for digital signatures and, once signed, will submit it to the Graduate School for processing of dissertator status. Students will receive an email confirmation from the Graduate School once the signed warrant has been submitted confirming dissertator status for the next semester.

DISSERTATOR STATUS

The Graduate School sets the minimum requirements and deadlines each semester for dissertator status:

https://grad.wisc.edu/deadlines/

https://grad.wisc.edu/documents/dissertator-status/

Dissertator status is effective at the start of the semester immediately following the completion of these requirements. In addition to the Graduate School requirements for dissertator status, the Physics program also requires students to:

• Pass the Qualifying Exam at the Ph.D. level
• Complete the required core coursework with a grade of B or better
• Satisfy the minor requirement
• Pass the Preliminary Exam

DOCTORAL DEGREE

Thesis Defense

The doctoral thesis defense is an oral defense of the dissertation. The thesis defense includes both a presentation of the dissertation material, and a question and answer sessions that can take place both in open session (in front of a general audience) and closed session (only the doctoral thesis committee). Graduate School policy requires that the thesis defense must be completed within five years of passing the Preliminary Examination. Details from the Graduate School about the final oral examination (thesis defense) can be found here:  https://grad.wisc.edu/documents/final-oral-examination/

The thesis defense also requires a warrant. Warrant requests must be made to the Graduate Coordinator at least three weeks prior to the date of the thesis defense.  The date, time, and location of the defense, as well as the dissertation title and committee members, must be finalized before requesting the warrant.

Thesis Committee

In accordance with Graduate School policy, the doctoral thesis committee consists of the student’s faculty advisor and three other committee members. The chair or one of the co-chair’s must be graduate faculty from the Department of Physics.  At least three of the members must be graduate faculty; at least one of the faculty must be from another graduate program.  Further details are available here: https://grad.wisc.edu/documents/committees/

The Graduate School doctoral guide outlines the specific formatting requirements for the dissertation as well as the steps to deposit the dissertation: https://grad.wisc.edu/current-students/doctoral-guide/

Degrees at UW-Madison are conferred three times during the year by academic term: Fall, Spring, & Summer.  The date the dissertation is deposited to the Graduate School determines the degree term.  The Graduate School degree deadlines are listed here: https://grad.wisc.edu/deadlines/

Degree Conferral & Payroll End Dates

The Graduate School policy on degree conferral and payroll end dates explains how students maintain tuition remission and the degree window period.

Graduate students should consult their faculty advisor, mentoring committee, the Associate Chair for Graduate Program, and/or the Graduate Coordinator about any concerns related to academic issues or the academic environment. Graduate students may also reach out directly to the Department Chair as an alternate approach. The hope is that this will result in the development of a working environment that all will find supportive. If graduate students have a question of whether or not a situation or discomfort should be discussed, the answer is YES! Any issue that is troubling should be addressed and, if it is within the Department’s authority, it will be resolved.

If a graduate student feels unfairly treated or aggrieved by faculty, staff, or another student, it is recommended that the concerns are first handled directly with the person responsible for the objectionable action, if possible. If the student is uncomfortable making direct contact with the individual(s) involved, the student should contact the faculty advisor or the person in charge of the unit where the action occurred (program or department chair, section chair, lab manager, etc.), and/or contact the people mentioned above.

There are also resources and formal grievance procedures at the campus level that can be followed, which are outlined in the Graduate School policies: https://grad.wisc.edu/documents/grievances-and-appeals/

The following resources may also be helpful in addressing concerns:

• Bias or Hate Reporting
• Graduate Assistantship Policies and Procedures
• Office of the Provost for Faculty and Staff Affairs
• Dean of Students Office  (for all students to seek grievance assistance and support)
• Employee Assistance  (for personal counseling and workplace consultation around communication and conflict involving graduate assistants and other employees, post-doctoral students, faculty and staff)
• Employee Disability Resource Office  (for qualified employees or applicants with disabilities to have equal employment opportunities)
• Graduate School  (for informal advice at any level of review and for official appeals of program/departmental or school/college grievance decisions)
• Office of Compliance  (for class harassment and discrimination, including sexual harassment and sexual violence)
• Office of Student Conduct and Community Standards  (for conflicts involving students)
• Ombuds Office for Faculty and Staff  (for employed graduate students and post-docs, as well as faculty and staff)
• Title IX  (for concerns about discrimination)

LEAVE OF ABSENCE

While in most cases participation in the program is continuous over time, students sometimes find it necessary to take a temporary leave of absence. Graduate students may request a leave of absence for one semester or for one year by submitting a form outlining the timeline for the leave and general reasons. The faculty advisor must agree that the student is leaving in good standing and may re-enter the program in a reasonable stated length of time. The Department Chair, in consultation with the Associate Chair for Graduate Program, will review all leave of absence requests.

If a student is granted a one semester leave of absence, the milestone due dates and terminal deadlines are pushed back one semester. If a student is granted a full year leave of absence, all due dates and deadlines are pushed back one year. Students may be granted a leave of absence for no more than one year at a time.  Students who do not register for more than one semester (Fall or Spring) will be considered inactive by Graduate School standards and must apply for re-entry.  Students who take a leave of absence and are in good standing are likely to be approved for re-entry upon return.  Prior funding guarantees may or may not continue to be in effect and will be decided in a case by case basis.  A leave of absence is not required for summer term as summer term is not a required term of enrollment if a student is not being paid as a graduate assistant or fellow.

Graduate students who leave the program in good standing for more than one term (not including summer) may request re-entry to the program by completing the Graduate School application for re-admission. Department leadership will review the request based on the information provided at the time the student plans to return.

The Graduate School outlines the policy for readmission for previously enrolled graduate students: https://grad.wisc.edu/documents/readmission/

Time Limits

In addition, the Graduate School specifies time limits for completion of current coursework and research.  Students who take a leave of absence or re-enter into the program should be aware of these policies: https://grad.wisc.edu/documents/time-limits/

The Department Chair has the authority to make individual exceptions to policies found in the PhD program handbook. Exceptions must involve extenuating and/or unique individual circumstances. Requests for such exceptions should be made in writing to the Associate Chair for Graduate Program from the student and/or faculty advisor.

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Ph.D. Qualifying Procedure for Advancement to Candidacy

There are two components to the qualification procedure, written and oral.  This page contains a summary.  For a complete description, please see the Physics Graduate Program Handbook.

Written Component

The purpose of this component is to assure that all students admitted to candidacy in the Department have a certain core competency necessary for success in a physics career.

The core courses are defined as Classical Mechanics (601), Mathematical Methods of Physics (605), Electrodynamics (606), Quantum I (614), Quantum II (615) and Statistical Physics (602).  Students must demonstrate competency in the core courses. 

Starting in Spring of 2023, and with permission of the Research Advisor and the Graduate Program Director , students are allowed to replace a 6NN core course with a research course for the purpose of written qualification. In this case, the core course that is replaced is waived altogether and excluded from the qualifying process. The intent of this option is to allow students to take at least one advanced course needed for their research before their third semester. You must have prior permission of your Research Advisor and the Graduate Program Director to exercise this option.

The resulting set of 6 courses define the “qualifying coursework.”

To qualify in coursework, a student must achieve the following:

• Pass Mathematical Physics (605) with a B- or better, assuming it is among the qualifying courses. 
• Of the remaining qualifying courses, all but one must receive a B or better for qualification. 
• The sixth course must be passed with a B- or better. 

In other words, a student with a B- in 605 and one other qualifying course would still qualify in coursework, so long as all other courses received a grade of B or better. Core courses that have been waived are treated as if they received a B or better for the purpose of qualifying.

In rare cases, a student may request a qualifying exam if they fail to pass a course.  Qualifiers will only be offered to students who have taken a course and failed to receive a B or better.  Because they are optional, Students must request a qualifying exam as soon as possible after receiving a low grade in a qualifying course . A request for an exam is also a commitment to take the exam: pulling out of this commitment is strongly discouraged and will result in denial of additional qual requests. 

Qualifying exams, if offered, take place shortly before the start of the corresponding core course. A passing grade on the qualifier is 55% or better. Passing the qualifier is equivalent to passing the course with a B or better.

Wherever possible, qualifying exams are graded double-blind, meaning that faculty do not know whose paper they are grading, and students do not know by whom their exams were graded.  All problems have at least two graders for quality control.

While the following is subject to change, qualifying exams are currently four hours long and comprised of three problems. They are closed book with no notes permitted. There is a 15 minute period before the exam when students may look over the problems but not write. Each of the problems has equal weight, but the weight of questions within each problem is not fixed and is determined in a case-by-case basis. 

In rare cases, and under exceptional circumstances, the department may opt to offer a student a "Q exam."  The goal of the Q exam is to help a student advance to candidacy when their course or final grades are close, but not quite sufficient to merit qualification.  In this case, the Graduate Curriculum Committee (GCC) will pose a question or questions to aid in focusing the student on their perceived areas of weakness. The student will prepare solutions to these problem and then be questioned on them, and related topics, at the Q exam.

Complete details of the coursework/written component of the quals, including the Q exam, can be found in the Physics Graduate Program Handbook .

A note about the role of the Graduate Curriculum Committee (GCC)

The GCC consists of faculty teaching graduate courses, plus the Graduate Program Director.  They have primary responsibility for both graduate curriculum and the qualification procedure.  Their responsibilities include the following:

• Providing guidelines for the the core graduate courses. This includes creation of a list of required topics to be covered in each course and ensuring that the guidelines are followed.
• Writing and administering mid-semester and end-of-semester student surveys for the core courses. The surveys will ask questions about coverage of material specific to the course and student understanding. The data are collected and reviewed by the GCC.
• Preparing and grading qualifying exams as needed.
• Recommending to the full faculty a pass/fail decision for each student for the coursework quals; 
• In rare cases, administering the Q exam as described in the Physics Graduate Program Handbook .

Impact on Financial Support

Failure to pass the written component of the Qualifying Procedure prior to the end of the fifth semester in the program will result in removal from the Physics doctoral program, but usually allowing one term to complete an M.S. degree, if necessary. Financial assistance cannot be guaranteed during any additional semester used to complete an M.S. degree.

Oral Component

The purpose of the oral/research component of the qualification procedure is to help students transition from formal coursework to engagement in research, and to develop specific skills necessary for success in research. This component can be scheduled any time after the completion of the coursework component, but no later than the 5th semester in the program.

With mutual consent of the student and research advisor, the Research/Oral component of the Quals may also serve as a Dissertation Prospectus presentation . In that case, the full dissertation committee must be formed and a written prospectus document prepared on the same timeline as above, but in the format and with the content of the prospectus (see Sec. II.9). Students are strongly encouraged to use this opportunity to complete their prospectus by the end of the fifth semester. However, the Research Quals must not be postponed if a prospectus cannot be completed by the end of the 5th semester.

To satisfy this requirement, students must do the following:

• Choose a Chair. Before the first day of the 5 th semester, students shall choose a faculty member to serve as Chair of their Research Qual Committee. Except in rare cases, this should be the same faculty member who serves as the Dissertation Committee Chair.  Identifying an appropriate chair is the responsibility of the student.  The chair will select one other faculty member to serve on the Research Qual Committee. The name of the chair will be communicated to the Graduate Program Director No later than September 1 before the beginning of the fifth semester .  If a student has difficulty identifying a chair, they must speak with the Graduate Program Director before the beginning of the fifth semester. Note that the role of the Research Qual Chair is not to supervise the study, but to be a source of advice and help.
• Propose a topic for the presentation. The student shall identify in consultation with the Chair, a research topic that is related to the anticipated subfield. They shall consult with the Chair of their Research Qual Committee to ensure that the topic is reasonable and the proposed presentation is of appropriate nature and scope.
• Schedule a presentation.The presentation is expected to reflect careful study of a current topic and to demonstrate that the student has understood both the important physical concepts, and the larger scientific context of the topic under investigation. A key element is the requirement that the student consult multiple research papers to put together a cohesive discussion of contemporary work or an open problem in physics. In other words, summarizing a textbook discussion is inappropriate, as is simply giving a summary of research that the student has already completed.
• A list of references used in the study must be provided to the Research Qual Committee.
• The length of the presentation should be 30-45 minutes, and students should expect additional time, typically 15-20 minutes, devoted to discussion with the committee. It may be scheduled any time after completion of the written component of the qualifying procedure and no later than the end of the fifth semester in the program .
• Following the presentation, the Chair of the student’s Research Qual Committee will send a completed Research/Oral Qualifying Exam Checklist to the GPD. If the presentation is deemed inadequate, the committee may ask the student to perform additional work, such as preparation of a short document or a second presentation, which must be completed by 15 December.

Department of Physics

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Course of Study

Guide to graduate study (yellow book).

Guide To Graduate Study (Yellow Book)

Graduate Courses

Graduate Students should consult with their special committee in choosing courses. Guidelines can be found in the "yellow book”.

General descriptions of the courses can be found in the  course catalog , and scheduling information in the  course/time roster .

Required Exams

As a graduate student you are expected to pass three examinations on the way to earning a Ph.D.

The first is a qualifying (Q) examination, an oral examination that serves as a check on your progress and as a diagnostic of possible weaknesses that need attention. It is administered at the start of the fall and spring semester. It should be taken by the start of your second semester. Please see the yellow book for more details.  You may have heard that at some schools the qualifying examination is used to pare down class size, to weed out students. This is never the case at Cornell. Each year, the physics department admits the number of graduate students that it anticipates being able to support throughout the length of their stay in the doctoral program. When you come to Cornell, you are secure in the knowledge that the department and your professors have made a valuable investment in your training. The faculty and staff are committed to helping you succeed.

The other two exams (A and B) are given by the members of your permanent special advising committee. The exams will be individualized and reflect the particular emphasis and direction of your program.

Special Committees

Initially, you will be assigned three faculty members who will act as your temporary Special Committee. Together they represent different disciplines within physics. As your research interests become more focused, and after you pass a qualifying examination (usually in your second year), you will invite faculty members to comprise your permanent Special Committee. Usually, you select three faculty members whose research interests you share. These professors will guide you both in designing a curriculum and in demonstrating proficiency through the required examinations. They alone will judge your progress toward a degree.

Your Special Committee will be chaired by a member of the graduate field of physics and include two other Cornell faculty members, only one of whom is required to be a member of the field. If, for example, you choose to complete a minor in applied mathematics or biology or chemistry, you may invite a professor from one of those fields to join your committee as the third member.

Learning Goals and Assessment

As part of your education, we want to ensure that first and foremost you know how to “think like a physicist”. This implies that you can synthesize knowledge from different areas, make educated guesses and take your hard-earned course-based knowledge to the next level, where you will apply it and knowledge that you acquire independently or with your mentors and peers to solve problems of interest. That is why we prefer a broad education and course base, and our education will prepare you for a career not just in the specific area that is your dissertation topic but our Ph. D. should prepare you for a career as a professional scientist, with all the flexibility that that implies.

Physicists must also learn how to communicate using written, spoken and presentation skills. You will acquire these skills as part of our course work (for example in Physics 6510, our Advanced Laboratory course has formal materials on how to carry out “Back of the envelope calculations” and a requirement to write lab reports in standard journal (Physical Review Letters) format as well as make a presentation to faculty and peers in a timed format. These formative skills are essential for the practicing Physicist.

Exams and assessment are part of the learning process. Formal learning in a classroom environment is assessed in exams that are a part of course work, and could be either take-home, timed in-class exams or term-papers combined with presentation of materials. The Q exam (see the section on exams) will assess your knowledge of Physics, ability to express yourself and communicate as well as your ability to analyze a problem, break it down into “bite sized components” and work through to obtain an acceptable solution. All of these will help faculty assess your success in transitioning from a “knowledge-acquirer” to a practicing physicist who can synthesize and attack complex problems as well create new knowledge by carrying out original research.

Feedback – How the results of assessment are used to alter / improve programs Your initial “special committee” also receives a “charge” from the DGS to provide feedback on the results of Q exams. The DGS also meets informally with the incoming class twice in the academic year to assess their perceptions and obtain their input. This information is then communicated to instructors to help improve outcomes.

Program success and metrics We compile statistics on the success of our students. We also continually strive to assess whether our effort to attract women and minorities is successful, and whether we are successful in guiding our students through to a Ph.D.

Physics graduate student

Stanford university.

I’m a graduate student interested in particle phenomenology and physics education. I spent two years in the UK as a Marshall scholar, and am currently a PhD student at Stanford, funded by an NSF Graduate Research fellowship. A complete CV is available here .

I got started by devouring the scifi section of my local public library, but it wasn’t until watching Particle Fever in college that I knew what I wanted to be. I find nothing more thrilling than the process of scientific discovery, whether it’s the “aha!” moment of a single student or the collective effort of the entire physics community, and I hope to be a lifelong participant as a professor of physics.

• Beyond the Standard Model
• Dark matter
• Precision experiments

PhD in Physics, 2024 (planned)

MSc in Mathematical and Theoretical Physics, 2019

MASt in Mathematics, 2018

BSc in Physics and Mathematics, 2017

Recent Papers

Physical signatures of fermion-coupled axion dark matter.

The axion-fermion coupling induces spin-dependent forces and torques, which can lead to macroscopic currents. “Magnetized multilayer” setups can use these currents to probe orders of magnitude beyond existing bounds.

Interactions of Particles with "Continuous Spin" Fields

Observed long-range forces are traditionally assumed to be mediated by fields with exactly zero spin scale. We present the first theory of matter particles interacting with “continuous spin” fields with arbitrary $\rho$, and show that there are calculable, universal, observable $\rho$-dependent modifications from familiar gauge theories.

Discovering QCD-Coupled Axion Dark Matter with Polarization Haloscopes

QCD axion dark matter induces oscillating EDMs, yielding physical currents that can be amplified in a microwave cavity. This setup has the unique ability to test whether a cavity haloscope signal arises from the QCD axion.

Probing Invisible Vector Meson Decays with NA64 and LDMX

Electron beam fixed target experiments such as NA64 and LDMX can improve constraints on invisible light vector meson decays by $5$ orders of magnitude, enhancing their sensitivity to dark matter of mass $m_\chi \gtrsim 0.1 \ \mathrm{GeV}$.

Quantum Field Theory I (Physics 330)

In Autumn 2022, I was the TA for Stanford’s introductory quantum field theory class, taught by Prof. Bernhard Mistlberger . We overhauled the course and produced new problem sets, which we believe strike a good balance between traditional particle physics applications, and connections to other fields. I also taught weekly sections which laid out the big picture and showed tricks for doing the problems efficiently.

• Problem sets: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 | Solutions: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9
• Very rough section notes: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10
• Final exam | Solutions

Physics Olympiad Handouts

I’ve developed a series of challenging problem sets for students aiming at gold medals at the International Physics Olympiad. They contain about 1,000 solved questions, explanations of problem solving techniques, hundreds of examples, and many references to historical and modern literature. For more details, see the syllabus and FAQ . Usually, students take a year to work through the handouts; to see if you’re ready, try the preliminary problems (answers here ).

Core Curriculum

• Problem Solving I ( Sol ), Problem Solving II ( Sol )
• Mech I ( Sol ), Mech II ( Sol ), Mech III ( Sol ), Mech IV ( Sol )
• Elec I ( Sol ), Elec II ( Sol ), Elec III ( Sol ), Elec IV ( Sol )
• Mech V ( Sol ), Mech VI ( Sol ), Mech VII ( Sol )
• Thermo I ( Sol ), Thermo II ( Sol ), Thermo III ( Sol )
• Elec V ( Sol ), Elec VI ( Sol ), Elec VII ( Sol )
• Relativity I ( Sol ), Relativity II ( Sol )
• Waves I ( Sol ), Waves II (Sol), Modern I ( Sol )

Supplemental Topics, Review, and Practice Olympiads

• Mech VIII ( Sol ), Elec VIII ( Sol ), Relativity III ( Sol )
• Waves III (Sol), Modern II ( Sol ), Modern III ( Sol )
• Mech Review ( Sol ), Elec Review ( Sol ), Other Review ( Sol )
• Oly-Mech ( Sol ), Oly-Elec ( Sol ), Oly-Other ( Sol )
• Final ( Sol )

Personal Notes

These are the notes I’ve taken while learning physics. I use them for reference, but they’re quite terse, and not a good resource to learn from. They weigh in at 1,900 pages and 750,000 words.

Undergraduate

These notes cover what I learned at MIT, through courses, lecture notes, and books.

• Undergraduate Physics
• Undergraduate Math
• Geometry and Topology
• Atomic and Optical Physics
• Solid State Physics
• Astrophysics
• Machine Learning

These notes follow courses taught at Cambridge’s Part III and Oxford’s MMathPhys.

• Group Theory
• Statistical Field Theory
• General Relativity
• Quantum Field Theory
• The Standard Model
• Supersymmetry
• String Theory

If you like the style, you can download a TeX template here .

• Learning Introductory Physics . A FAQ for high school students who want to start learning physics or taking part in physics competitions, such as the USAPhO.
• After Introductory Physics . Some tips for self-taught students on what to do after mastering the basics, including book recommendations and online resources.
• Physics Activities . Some places you can apply your physics knowledge in high school.
• The Theoretical Minimum . A short list of canonical books you could self-study, to go from the level of introductory physics to PhD candidacy.
• The Stanford Physics Qualifying Exam . A transcript of my PhD qualifying exam, and advice.
• Cosmological Relaxation . A dissertation written for the Oxford MSc in Mathematical and Theoretical Physics, covering models that “relax” the Higgs boson’s mass. Also contains unqualified musings on model building and the meaning of naturalness and fine-tuning.
• The Meaning of Nothing . The New College Demuth prize essay, on how theoretical stories map onto reality, and why a physicist’s philosophical flexibility is a useful tool. Published in the New College Record with a wonderful illustration by Audrey Effenberger .
• Here are some memorable articles about science and everything else .
• Here are some fun videos for a rainy day.
• My 1,000 answers on Physics StackExchange have 2 million views; here’s a sample .
• [email protected] (research-related)
• [email protected] (everything else)

Doctoral Qualifying Exams

These requirements apply to the Physics, Astrophysics, and Physics Education tracks. The  Chemical Physics  track has separate requirements.

Basic Proficiency Requirement

The doctoral candidates in our PhD program must demonstrate proficiency in the core areas. There are four common core areas for the Physics, Astrophysics, and the Physics Education Track: Classical Mechanics, Electricity & Magnetism, Quantum Mechanics, and Statistical Mechanics. Students in the Astrophysics Track must demonstrate proficiency also in the Astronomy area (AST121, AST122) in addition to the aforementioned areas.

Proficiency in a given area may be demonstrated in one of two ways: (i) By passing the relevant course(s) with an average grade of A- (3.67) or better; or (ii) By passing a special examination in the subject (i.e., the written qualifying exam). In addition, a student who achieves an overall average grade of A- or better in Classical Mechanics (PHY131) and Electricity & Magnetism (PHY145, PHY146) will be exempt from the examinations in both areas, and a student who achieves an overall average grade of A- or better in Statistical Mechanics (PHY153) and Quantum Mechanics (PHY163, PHY164) will be exempt from the examinations in both of those areas. For students in the Astrophysics and Physics Education tracks, the Electricity & Magnetism and Quantum Mechanics components will be based on grades in PHY145 and PHY163. A student in the Astrophysics track who achieves an overall average grade of A- or better in the astronomy courses (AST121, AST122) will be exempt from the examinations in the Astronomy area.

Suppose a student on the regular physics track receives the following grades:

• Phys 131 Classical Mechanics B+ (3.33)
• Phys 145 Electricity & Magnetism 1 A (3.67)
• Phys 146 Electricity & Magnetism 2 A (4.00)
• Phys 153 Statistical Mechanics B (3.00)
• Phys 163 Quantum Theory 1 A (3.67)
• Phys 164 Quantum Theory 2 A (4.00)

Because the overall average for 131, 145 and 146 is 3.67, this student is exempt from the examinations in both Classical Mechanics and Electricity and Magnetism, even though the grade in 131 is below A. The overall average for 153, 163, 164 is 3.56, below the threshold for exemption from both exams. The average in 163 and 164 is above A, so the student is exempt from the examination in Quantum Mechanics. But because the grade in 153 is below A, this student will need to take an examination in Statistical Mechanics.

If the student does not achieve a satisfactory grade in the relevant areas, a written qualifying exam in the area will be delivered to assess the proficiency of the doctoral candidate. At the end of each semester, it is the responsibility of the Director of Graduate Studies of the department to identify the students in need of the written qualifying exam(s). The Director of Graduate Studies will then notify the students, their advisors, and the relevant qualifying exam committee. The students and the qualifying exam committee have three weeks to schedule the written qualifying exam, which will normally take place within six weeks of the start of the next semester. Any postponements must be approved by the Director of Graduate Studies.

For each core area, there will be a qualifying exam committee appointed by the Chair of the department. The members of the committee will typically be selected from the faculty members who have recently taught the associated courses.

The content of each exam should be consistent with the requirements of the degree tracks in which the students taking the exam are enrolled, and should test the student's general understanding and command of the concepts, principles, and phenomena of the topic, focusing on the fundamental understanding, and including questions at a range of levels from advanced undergraduate to graduate level. The written qualifying exam is not intended to be the equivalent of a final examination for the graduate course(s). The qualifying exam committee is responsible for writing an exam consistent with these goals. The chair(s) of the qualifying exam committee(s) may solicit draft questions from the entire Physics and Astronomy faculty body for possible inclusion in the exam. This will be amended and incorporated at the discretion of the committee(s). The Department Administrator shall maintain a collection of past exams given for each subject. A sample of three past exams in each area will be made available to students.

At the time of scheduling, the qualifying exam committee will inform the student(s) of the format, content, and duration of the examination. The duration of exams should be no less than two and no more than four hours if it deals with material from a single course, and no more than six hours if it deals with material from two courses. The qualifying exam committee will inform the Director of Graduate Studies of the results of the exam, and whether or not the student has met the proficiency requirement. The Director of Graduate Studies will communicate the outcome to the student and his/her advisory committee, and will discuss future developments.

Ordinarily, a student will have only one opportunity to pass the examination in any given area. Under exceptional circumstances, a student who does not pass may appeal to the examination committee for an opportunity to take a second examination.

Mathematics

Congrats to 2024 outstanding teaching assistants.