# Qualifying Exam

**General Information**

The qualifying exam is designed to assess students' understanding of core topics in physics at the advanced undergraduate level. The exam process provides students with an opportunity to collate course work, to gain confidence in skills, and to solidify knowledge underlying advanced course work and ultimately significant advances by UW-Madison physics graduates. The exam is thus part of the assessment of the achievement of the department's learning goals for both the Master's and Ph.D. programs.

The exam is a written exam that is offered twice a year. The exam covers four core topics: Classical Mechanics (CM), Electricity and Magnetism (EM), Statistical Mechanics (SM), and Quantum Mechanics (QM). Each exam topic can be passed independently of the others. The nominal passing score for each area is 60% for the pursuit of the doctoral degree and 50% for the pursuit of a M.S. or M.A. degree. Entering Ph.D. students are required to take the exam in their first semester in the program. Students are expected to consult with their advisor/mentor and the Director of Graduate Studies following the initial assessment.

All physics Ph.D. students will have four opportunities to pass the written exam at the Ph.D. level, within their first two years in the program. Physics graduate students that pass the written exam at the Ph.D. level are automatically qualified to continue in the Ph.D. program. However, in the case that a student does not pass all four topics of the written exam after the four attempts, the next step is that the student has the option to request an appeal.

**Exam Structure and Topics**

The qualifying exam is a 6 hour exam that will be held over one full day. The exam consists of four sections, each lasting 1.5 hours, that each focus on one of the four core topics.

Two of these sections (CM and QM) will be held in the morning, and two (EM and SM) will be held in the afternoon, separated by a lunch break. There will be a quick 15-minute break between the two sections of the exam in both the morning and the afternoon sessions.

Each section of the exam is comprised of five problems. Students have to answer the first two problems, which are on elementary level undergraduate material [Physics 200-299 level], and answer two other problems (out of three offered) on intermediate/advanced undergraduate material [Physics 300-499 level]. The first two problems count one third of the total score, and the second two problems chosen count the remaining two thirds of the total score.

The areas covered for each topic include (i) CM: motion in electromagnetic and gravitational fields, rigid bodies, coupled oscillations, and continuum vibrations; (ii) EM: statics, fields in matter, Maxwell's equations, light and optics, radiation, and circuits; (iii) SM: thermodynamics and statistical mechanics of matter and radiation; (iv) QM: wave mechanics, matrix mechanics, observables and measurements, angular momentum, perturbation theory, atoms and molecules, and scattering.

Courses in the department that are representative of this scheme are: (i) Physics 207 or 247, and 311 (CM); (ii) Physics 241 or 249, and Physics 448-449 or 531 (QM); (iii) Physics 208 or 248, and 322 (EM -- includes optics at the 200 level); (iv) Physics 207 and 415 (SM).

Typical textbooks at the 207/208 or 247/248 level:

*Physics: Principles and Applications*by Giancoli*University Physics*by Bauer and Westfall*Physics*by Resnick, Halliday, and Krane

Typical textbooks at the 241/249 level:

*Modern Physics*by Tipler*Modern Physics*by Krane*Modern Physics*by Harris

Typical textbooks at the 311 level:

*Dynamics of Particles and Systems*by Marion and Thornton*Classical Mechanics*by Taylor*Classical Mechanics: A Modern Perspective*by Barger and Olsson

Typical textbooks at the 322 level:

*Introduction to Electrodynamics*by Griffiths*Electricity and Magnetism*by Purcell*Classical Electricity and Magnetism*: A Contemporary Perspective by Barger and Olsson

Typical textbooks at the 415 level:

*Thermal Physics*by Kittel*Fundamentals of Statistical and Thermal Physics*by Reif*An Introduction to Thermal Physics*by Schroeder

Typical textbooks at the 448/449/531 level:

*Quantum Physics*by Gasiorowicz*Introduction to Quantum Mechanics*by Griffiths*Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles*by Eisberg and Resnick*A Modern Approach to Quantum Mechanics*by Townsend

**Exam Preparation**

Students are encouraged to consult their advisors and the Director of Graduate Studies about good practices for preparing for the qualifying exam. Previous exams will be available for study; please contact the Director of Graduate Studies if you need access. Outside reading, auditing or taking appropriate UW-Madison courses, and possible exam and group problem solving sessions are typical strategies for students requiring additional preparation. Students with special requirements must consult with the Director of Graduate Studies and the Graduate Student Coordinator at least two weeks prior to the exam date.

Students who fail to pass any of the topics of the qualifying exam on the first attempt will be encouraged to register for Physics 801 (Problem Solving in Modern Physics). This course will review the core topics at a rapid pace and will provide an opportunity to strengthen "qualifier-like" problem solving skills. It is to be offered in both the Fall and Spring semesters.

**Grading Policies and Retakes**

The qualifying exam is to be graded anonymously by faculty. The Graduate Qualification Exam Committee (QEC) collects all graded problems for all the students and reviews them in detail for consistency. Only after this thorough review will the final grade of pass or fail of each topic area be assigned. After this point, the results are unblinded and distributed.

Students may appeal for re-grades of specific exam problems to the Chair of the QEC at any point within two weeks after the exam is returned. Students should be aware that the partial grading metrics that are assigned by faculty for individual problems, which will also be reviewed by the QEC prior to the final pass or fail score assignments, will generally be respected unless there are obvious inconsistencies or errors.

In the case of failing scores on one or more core topics of the exam, in subsequent attempts students need to take only the portions of the exam in the topic area or areas that remain to be passed.

**Final Appeal Process**

If a student does not pass all four topical areas of the written qualifying exam at the Ph.D. level after four exam attempts, the next step in the process is that the student can request an appeal. The appeal process will be handled by a committee that consists of a faculty member of the student's choosing, and two other other faculty members that will be determined on a case-by-case basis. The appeal process will involve a broad assessment of the student's progress in the graduate program that includes the student's prior qualifying exam results, performance in graduate coursework, and progress to date in research. Upon a careful evaluation of these factors, the appeals committee will make the final recommendation as to whether or not the student has achieved qualification status in the Ph.D. program. If the appeals committee decision is positive, the student has passed the Qualifying Exam requirement in the department, as required for good standing and satisfactory progress toward the Ph.D.