Written Qualifying Exams

Your first attempt at the written qualifying exams usually takes place during the two weeks before the start of classes. Exams are three hours each, spaced out every other day to give time for rest and study.

Continuing studends lead a series of group study sessions called Written Qual Bootcamp prior to the exams. Each study session is a few hours long, and specializes in problems for each Qualifying Exam. New students are encouraged to attend if available!

• Exams are closed-book

• Crib sheets are provided

• Calculator

• Water

• Blank paper

• Pencils/pens

• Each section is a three hour, closed-book written examination, with one sheet of information (formulae, equations, etc.) provided.

• You pick two out of three questions to solve for each exam.

• Each question is worth 10 points maximum.

• A score of 12 or higher on each exam is passing.

• If you pass one exam area, you do not need to take that exam again.

You do not need to take all five exams at once - you can space out your attempts.

If you choose to space out your attempts, first-year students are encouraged to take

on their first attempt:

• Classical Mechanics

• Math Methods

• Electricity & Magnetism

and on your second attempt:

• Quantum Mechanics

• Statistical Mechanics

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, 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.

Please contact the Disability Resource Center (DRC) for exam accommodations, like extra time, light or noise-sensitive spaces, exams in alternative formats, etc. You do not need to share confidential medical information with the Physics Department or faculty. Instead, meet with the DRC who will make recommendations to the department based on an evaluation of your needs.

Please allow 2-3 weeks to meet with the DRC and make departmental recommendations.

 You may petition the Graduate Committee to waive a course if:

• you score very high on the associated written qualifying examination;

• you took the equivalent graduate-level course at your prior institution and obtained a satisfactory grade;

• the course covers the material in the first-year courses syllabi.

Email the Graduate Committee Chair with your written qual score, unofficial transcript showing the equivalent graduate-level course, and a copy of the syllabus from that course.

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.

Thermodynamics

• The zeroth, first, and second law

• Carnot engines

• Entropy

• Equilibrium and thermodynamic potentials

• Stability conditions

• The third law

Probability

• Random variables

• Probability distributions

• Many random variables

• Sums of random variables and the central limit theorem

• Rules for large numbers

• Information, Entropy, and Estimation

Kinetic theory of gases

• Liouville’s theorem

• The Boltzmann equation

Classical statistical mechanics

• 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

Quantum statistical mechanics

• 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 He4

Interacting particles

• 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 (1st and 2nd order),  Critical behavior, Exponents

Statistical fields

• • The Landau theory of 2nd 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

Fluctuations

• Scattering and fluctuations

• Correlation functions and susceptibilities

• Fluctuation corrections to the saddle point

Textbooks and References:

• 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

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.

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

• Complex variables (particularly contour integration, and topics such as convergence of series, etc.)

• Laplace transforms

• Fourier analysis

• 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.

Jackson, Classical Electrodynamics, esp. chapters 1-9, 11-14 (in principle, anything in the text may be covered in the exam).