Preliminary Examination Information

Physics Preliminary Exam

The 2025 Preliminary Exam is scheduled for May 27–30, 2025.

*** Baylor Physics Ph.D. Students can find additional logistical details and FAQs here: Baylor Prelim Info Presentation ***

The Physics Preliminary Exam for admission to candidacy for the Ph.D. will be given over the course of four days. The exam consists of four parts: Part I (Classical Mechanics), Part II (Quantum Mechanics), Part III (Electricity and Magnetism), and Part IV (Statistical Mechanics).

Physics Ph.D. students who will have completed their first-year of study in May and have not already passed all four parts of the exam must take the exam. Students working toward the terminal Masters degree may take the exam in place of an oral exam.

Each part of the exam will consist of 5 problems. All 5 problems will be scored.

The Physics Department will provide the following for use during the exam:  a simple scientific calculator (TI-30XA), Schaum’s Mathematical Handbook of Formulas and Tables (Spiegel et al.), and The Cambridge Handbook of Physics Formulas (Woan).

The topics covered by the four parts of the Preliminary Exam are listed below.

Exams from previous years are available on the web in a PDF file. The exams from 2020 to 2024) may be downloaded from the file located at

Older exams in a different format (6 problems for each part) are available at

Even older versions (from 1967 till 2006) are available at

Since these documents are long, please conserve paper by printing specific pages only as you use them.

Best regards,

The Preliminary Exam Committee

Part I. Classical Mechanics

The Classical Mechanics (CM) part of the Preliminary Exam will test basic concepts of classical mechanics and related applications to physical problems. The exam will cover both (i) material presented in PHY 5320 (the first semester of graduate CM at Baylor) and (ii) material generally presented at the undergraduate level. The topics that may be covered in the exam are those implied by the learning outcomes given in the list below.

The graduate level at which these topics will be covered is on par with Goldstein, Poole & Safko, Classical Mechanics. The level of the undergraduate material in the exam is representative of that found in typical undergraduate textbooks such as Thornton & Marion in Classical Dynamics.

1. The student will demonstrate a knowledge of linear mechanics in a Newtonian framework, including the equation(s) of motion, momentum, energy, and work.
2. The student will demonstrate how to calculate the Lagrangian for a system and analyze or apply the resulting equations of motion. *
3. The student will demonstrate how to develop and convert a Lagrangian into a Hamiltonian and analyze or apply the resulting equations of motion. *
4. The student will determine the symmetries of a problem and use them to simplify the process of calculating equations of motion and identifying constants of the motion (if applicable).
5. The student will demonstrate how to determine the normal modes in a damped and/or driven oscillating system.
6. The student will demonstrate how to calculate the moment of inertia of an object, the torques applied to it, and apply the resulting equations of motion. *
7. The student will demonstrate how to solve elastic and inelastic collisions.
8. The student will demonstrate how to use the equivalent one-body problem to solve equations of motion in a central force system.
9. The student will demonstrate the use of Lorentz transformations, including the concepts of length contraction and time dilation, to simplify and solve special relativity problems.

*Examples of “analyze or apply the resulting equations of motion” include analysis of motion in limiting cases, calculating work done by constraint force, finding position where constraint force is broken (ex: ball rolls off a sphere), finding constants of the motion, determining equilibrium points, determining period of motion, finding oscillation frequency, etc.

Part II. Quantum Mechanics

The Quantum Mechanics (QM) part of the Preliminary Exam will test basic concepts of quantum mechanics and related applications to physical problems. The exam will cover both (i) material presented in PHY 5370 and (ii) material generally presented at the undergraduate level. The topics that may be covered in the exam are those implied by the learning outcomes given in the list below.

The graduate level at which these topics will be covered is on par with Sakurai and Napolitano, Modern Quantum Mechanics, Chapters 1-4. Good references for applications are the Complements sections in Cohen-Tannoudji et al., Quantum Mechanics, Volume I. The level of the undergraduate material in the exam is representative of that found in typical undergraduate textbooks such as Griffiths, Introduction to Quantum Mechanics (which is used in PHY 3372–3373); Gasiorowicz, Quantum Physics; or Shankar, Principles of Quantum Mechanics.

1. The student will be able to apply fundamental concepts of quantum mechanics to predict experimental outcomes for measurements of observables on simple quantum systems.
2. The student will be able to apply the uncertainty principle and distinguish compatible and incompatible observables.
3. The student will be able to compute the bound and/or unbound states for a given Hamiltonian.
4. The student will be able to derive the eigenstates of the angular momentum operators and prove completeness and orthogonality.
5. The student will demonstrate the use of symmetries, both discrete and continuous, in quantum mechanics.
6. The student will demonstrate the use of time-independent perturbation theory and apply it to problems in quantum mechanics at the undergraduate level.
7. The student will demonstrate the use of time-dependent perturbation theory and apply it to problems in quantum mechanics at the undergraduate level.
8. The student will be able to apply approximation methods including the WKB method and the variational principle at the undergraduate level.
9. The student will be able to apply quantum mechanics to identical particle systems.

Part III. Electricity and Magnetism

The Electricity & Magnetism (E&M) part of the Preliminary Exam will test basic concepts of electricity and magnetism and related applications to physical problems. The exam will cover both (i) material presented in PHY 5330 (the first semester of graduate E&M at Baylor) and (ii) material generally presented at the undergraduate level. The topics that may be covered in the exam are those implied by the learning outcomes given in the list below.

At the graduate level, problems will be based at the level of Jackson, Classical Electrodynamics, Chapters 1–6. There may be undergraduate-level problems on any of the topics listed below. The undergraduate material on the exam is representative of that found in textbooks such as Griffith, Introduction to Electrodynamics, Marion & Heald, Classical Electromagnetic Radiation, and Schwartz, Principles of Electrodynamics. Also, topics like partial wave techniques and scattering are covered in many quantum mechanics textbooks.  Most undergraduate textbooks use the MKS (SI) system while graduate-level texts use the Gaussian system. You are expected to know the difference between the two systems; however, you are free to use the formulas in either system of units.

1. The student will demonstrate how to solve electrostatics problems for symmetric systems, including forces, image charges, system energies, and capacitances.
2. The student will demonstrate how to solve magnetostatic problems for symmetric systems, including forces, system energies, and inductances.
3. The student will demonstrate how to apply Ampere’s law and Faraday’s law to current distributions and circuits.
4. The student will demonstrate how to apply boundary conditions and solve problems for systems with uniform conductive materials and dielectric materials.
5. The student will demonstrate how to develop and use multipole expansions for charge distributions.
6. The student will demonstrate how to evaluate and use magnetic dipole moments for current distributions.
7. The student will demonstrate how to formulate the macroscopic Maxwell equations in terms of scalar and vector potentials.
8. The student will demonstrate the meaning and application of retarded and advanced Green’s functions.
9. The student will demonstrate how to formulate electromagnetic waves in dispersive and conductive materials (using Maxwell’s equations?)
10. The student will demonstrate how to solve problems with magnetic materials and boundary conditions, including permeability and magnetization.
11. The student will demonstrate how to use the Poynting vector to understand energy flow across boundaries at the undergraduate level.
12. The student will demonstrate how to formulate plane electromagnetic waves and polarization and use them to derive reflection and transmission coefficients at the undergraduate level.
13. The student will demonstrate the electromagnetic radiation of systems and particles using multipole formalism at the undergraduate level.
14. The student will demonstrate how to derive the scattering and diffraction cross sections at the undergraduate level.

Part IV. Thermal Physics and Statistical Mechanics

The Statistical Mechanics (SM) part of the Preliminary Exam will test basic concepts of statistical mechanics and thermal physics. The exam will cover both (i) material presented in PHY 5340 (graduate Statistical Mechanics at Baylor) and (ii) material generally presented at the undergraduate level. The topics that may be covered in the exam are those implied by the learning outcomes given in the list below.

The graduate level at which these topics will be covered is on par with Pathria, Statistical Mechanics and Huang, Statistical Mechanics. The level of the undergraduate material in the exam is representative of that found in typical undergraduate textbooks such as Kittel and Kroemer, Thermal Physics, Reif, Fundamentals of Statistical and Thermal Physics; Morse, Thermal Physics, Schroeder, An Introduction to Thermal Physics (which was used in PHY 4340); or Bowley and Sanchez, Introductory Statistical Mechanics.

1. The student will be able to demonstrate/describe the concepts of temperature, thermal equilibrium and the four laws (zero, one, two and three) of thermodynamics.
2. The student will be able to interpret PV and TS diagrams for a heat engine cycle, describe/calculate what happens in an engine for each leg of a cycle, evaluate the efficiency and/or coefficient of performance for engines and refrigerators, and compare it to the Carnot efficiency as appropriate.
3. The student will be able to identify the appropriate thermodynamic potential for a given system/process and compute intensive and extensive variables from it.
4. The student will be able to perform calculations to determine quantities like average kinetic energy, root mean square velocity, and pressure based on kinetic theory.
5. The student will be able to compute the partition function for standard systems of distinguishable and indistinguishable particles and derive thermodynamic properties from it.
6. The student will be able to identify the equilibrium conditions for 1st order phase transitions, apply the concept to find the pressure dependence of the transition temperature, and solve problems involving these concepts.
7. The student will be able to recognize phase-space as the appropriate framework for ensemble theory and be able to compute the number of microstates and the density of states for standard microcanonical ensembles using phase-space considerations.
8. The student will be able to describe the properties of Bose-Einstein and Fermi-Dirac systems, compute blackbody radiation from the ultra-relativistic Bose gas, and compute Fermi energy and occupation numbers for simple Fermi systems in the low temperature limit.
9. The student will be able to identify appropriate ensembles (microcanonical, canonical, and grand canonical) from the ensemble theory, corresponding to a given equilibrium condition and obtain mean values of statistical variables as well as fluctuations around the mean values.
10. The student should be able to treat the indistinguishability of identical particles classically and quantum-mechanically and to calculate mean occupation numbers and their fluctuations in the grand canonical ensemble.
11. The student should be able to apply the statistics of the occupation numbers to demonstrate the conditions allowed/unallowed for BE condensation in various elementary settings. Likewise, the students should be able to apply the statistics of the occupation numbers to the FD systems and describe zero temperature behaviors as well as deviation at non-zero (low) temperature.

Mathematical Methods

All Math Methods learning outcomes will be demonstrated by their application to physics problems in Classical Mechanics, Quantum Mechanics, Electricity and Magnetism, and Thermal Physics & Statistical Mechanics. This will test basic concepts of mathematical physics at the level of Butkov, Mathematical Physics, Arfken and Weber, Mathematical Methods for Physicists, or Wyld, Mathematical Methods for Physics. The topics that may be covered in the exam correspond to the material presented in PHY 5360 Mathematical Physics (the first semester of graduate Mathematical Physics at Baylor) and are those implied by the learning outcomes given in the list below.

1. The student will demonstrate the calculation of vector calculus derivatives such as the gradient, divergence, curl, and Laplacian in Cartesian, spherical, and cylindrical coordinates.
2. The student will demonstrate the application of Gauss' Theorem and/or Stokes' Theorem.
3. The student will demonstrate the application of analytic functions to physics.
4. The student will use the Cauchy integral theorem, Cauchy integral formula, or the residue theorem to calculate the value of a real-valued or complex-valued integral.
5. The student will demonstrate the application of the Fourier transform to physics.
6. The student will demonstrate that they can calculate a Fourier transform or inverse Fourier transform.
7. The student will demonstrate that they can calculate a Laplace transform or inverse Laplace transform (Bromwich Integral).
8. The student will demonstrate solutions to homogenous elliptic, parabolic, or hyperbolic partial differential equations in Cartesian, spherical, and cylindrical coordinates using separation of variables and/or the method of eigenfunction expansion.
9. The student will demonstrate the construction of a Green’s Function of a Sturm-Liouville ordinary differential equation. 
10. The student will demonstrate the calculation of the eigenvalues and eigenvectors of a matrix.