APS Graduate Exam study guide
APS Graduate Exam · Work through your exam, one topic at a time.
The APS Graduate Exam is a multiple-choice assessment designed to test whether a candidate has the working physics knowledge expected at the start of graduate-level study or in a research-adjacent technical role. It is aimed at physics graduates, engineering graduates moving into physics-heavy work, and independent learners who want an external check on their grasp of core theory. The APS Graduate Exam study guide has 6 sections and about 1,624 words.
01General Physics Fundamentals
This domain rewards dimensional fluency and order-of-magnitude reasoning. Know Newton's laws as statements about net force and momentum change, conservation of energy and momentum, the distinction between scalar speed and vector velocity, and the kinematics equations for constant acceleration.
288 words, about 1 min02Classical Mechanics
Expect Newtonian dynamics in one and two dimensions, work–energy and impulse–momentum theorems, conservation laws, rotational motion (torque, moment of inertia, angular momentum), gravitation and orbits, simple harmonic motion, and an introduction to Lagrangian mechanics. Know when each conservation law applies and what symmetry underlies it: time translation gives energy conservation, spatial translation gives momentum, rotational invariance gives angular momentum.
268 words, about 1 min03Electricity and Magnetism
Master Coulomb's law, electric field and potential, Gauss's law and symmetry, capacitance and energy storage, DC circuits (Kirchhoff's rules, series/parallel), magnetic force on moving charges and currents, Ampère's law, Faraday's law of induction, and Maxwell's equations in integral form. Understand that electric potential is a scalar and superposition is easier with it than with fields.
270 words, about 1 min04Quantum Mechanics
Understand wave–particle duality, the de Broglie relation λ = h/p, the photoelectric effect, the Schrödinger equation, wavefunctions and normalization, expectation values, the infinite square well, the harmonic oscillator, and the hydrogen atom. Know operators for position, momentum, and energy, and the meaning of commutation relations.
263 words, about 1 min05Thermodynamics and Statistical Mechanics
Know the laws of thermodynamics, the distinction between state functions and path functions, the ideal gas law, heat capacities at constant volume and pressure, entropy, Carnot efficiency, and the canonical ensemble. Understand that temperature is ∂S/∂E, that entropy counts microstates (S = k ln Ω), and that the Boltzmann factor e^(−E/kT) sets populations of energy levels.
277 words, about 1 min06Mathematical Methods and Laboratory/Experimental Physics
This domain blends mathematical technique with experimental practice. Know vector calculus (gradient, divergence, curl), linear algebra (eigenvalues, matrices, orthogonality), differential equations (first-order separable, second-order linear with constant coefficients), Fourier series and transforms, and complex numbers.
258 words, about 1 min