Physics GRE Prep & Study Guide

Physics GRE overview

The Physics GRE (PGRE) is a standardized subject test used by many U.S. graduate physics programs. A high score signals broad undergraduate mastery across classical mechanics, electromagnetism, quantum mechanics, thermodynamics/statistical mechanics, relativity, laboratory methods, and specialized topics. This guide is a structured, formula-first review you can use alongside timed practice sets.

Approximate topic distribution

Classical mechanics formula sheet

Newton II:                 F = dp/dt = ma
Work–energy:               W = ∫ F·dr = ΔK
Conservation:              E = K + U  (conservative forces)
Simple harmonic motion:    x(t) = A cos(ωt + φ),  ω = √(k/m)
Physical pendulum:         ω = √(mgd/I)
Central force orbits:      L = μ r² θ̇  conserved
Kepler III:                T² = (4π²/GM) a³
Lagrangian:                L = T − V,  d/dt(∂L/∂q̇) = ∂L/∂q
Hamiltonian:               H = p q̇ − L

Electromagnetism essentials

Coulomb / field:           E = (1/4πε₀) q r̂ / r²
Gauss’s law:               ∮ E·dA = Q_enc / ε₀
Potential:                 V = −∫ E·dl ,  E = −∇V
Biot–Savart:               dB = (μ₀/4π) I dl × r̂ / r²
Ampère–Maxwell:            ∮ B·dl = μ₀(I_enc + ε₀ dΦ_E/dt)
Faraday:                   ∮ E·dl = −dΦ_B/dt
Poynting:                  S = (1/μ₀) E × B
Wave speed:                c = 1/√(μ₀ε₀)
AC impedance:              Z = R + i(ωL − 1/ωC)

For a deeper conceptual walkthrough of electrostatic fields, see the Electric Field Guide & Visualizer.

Quantum mechanics checklist

• Postulates: states as kets, observables as Hermitian operators, Born rule probabilities.
• Infinite well: E_n = n²π²ℏ² / (2mL²), nodes = n−1.
• Harmonic oscillator: E_n = ℏω(n + 1/2).
• Hydrogen: E_n = −13.6 eV / n², degeneracy n² (ignoring spin).
• Commutators: [x, p] = iℏ, angular momentum algebra [J_i, J_j] = iℏ ε_ijk J_k.
• Spin-1/2: Pauli matrices, Stern–Gerlach intuition, addition of angular momenta.

Thermodynamics & statistical mechanics

First law:                 ΔU = Q − W  (sign convention dependent)
Ideal gas:                 PV = NkT = nRT
Entropy (Clausius):        dS = đQ_rev / T
Maxwell–Boltzmann:         f(v) ∝ v² exp(−mv²/2kT)
Partition function:        Z = Σ_i e^{−βE_i},  β = 1/kT
Helmholtz free energy:     F = −kT ln Z = U − TS
Equipartition:             (1/2)kT per quadratic degree of freedom

High-yield exam strategy

1. Drill dimensional analysis and limiting cases first — many PGRE items reward quick elimination.
2. Memorize order-of-magnitude constants (ℏc ≈ 197 MeV·fm, k ≈ 8.6×10⁻⁵ eV/K, α ≈ 1/137).
3. Practice under timed conditions — roughly 1.7 minutes per question across ~100 items.
4. Rotate weak topics weekly instead of re-reading only mechanics comfort zones.
5. Use interactive tools while reviewing — plot potentials with the graphing calculator and explore ODE phase structure with the phase portrait generator.

Two-week intensive outline

• Days 1–3: Mechanics + oscillations + central forces
• Days 4–6: E&M (electrostatics through Maxwell)
• Days 7–8: Quantum + atomic spectra
• Days 9–10: Thermo/stat mech + lab methods
• Days 11–12: Optics, waves, relativity
• Days 13–14: Full practice exams + error logs

For hands-on practice visualization, use the graphing calculator to plot potentials and waveforms, the phase portrait generator for dynamical systems, and the time graphing tool for position–velocity–time curves.

Bookmark this page as a formula cockpit, then jump into practice sets and interactive visualizations to convert recognition into speed.