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GRE Physics Subject Test

Study notes, worked examples, and practice questions across the GRE Physics domains, each with its sources cited. ETS describes the Physics Subject Test as a 2-hour computer-delivered test with approximately 70 five-choice questions.

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The syllabus

GRE Physics preparation, organized into the content areas below.

  1. 01

    Classical mechanics

  2. 02

    Electromagnetism

  3. 03

    Quantum mechanics

  4. 04

    Thermodynamics

  5. 05

    Optics and waves

  6. 06

    Atomic physics

  7. 07

    Special relativity

  8. 08

    Lab methods

Representative topics

Newtonian mechanicsMaxwell equationsSchrodinger equationStatistical mechanicsWave opticsHydrogen atomLorentz transformations

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Study content

The pages below are available without an account. Exam facts and technical concepts identify their official or open educational sources on the page.

Newton's Second Law and Free-Body Diagrams

A free GRE Physics mechanics note on applying net force, mass, acceleration, and free-body diagrams without hiding assumptions.

  • Choose the system whose motion is being analyzed.
  • Separate external forces from forces internal to the chosen system.
  • Apply the vector form of Newton's second law component by component.

Formulas covered: Newton's second law for constant mass

Read the Newton's Second Law and Free-Body Diagrams note

Energy and Momentum Conservation

A free GRE Physics mechanics note on the work-energy theorem, mechanical energy conservation, momentum conservation, and elastic versus inelastic collisions.

  • Apply the work-energy theorem to relate net work to a change in speed.
  • Decide when mechanical energy is conserved and when nonconservative work must be accounted for.
  • Write momentum conservation as a vector equation for an isolated system.

Formulas covered: Work-energy theorem · Conservation of mechanical energy · Linear momentum · Momentum conservation for an isolated system · Perfectly inelastic collision

Read the Energy and Momentum Conservation note

Simple Harmonic Motion

A free GRE Physics note on the simple harmonic motion equation, angular frequency for springs and pendulums, energy exchange in SHM, and qualitative damping.

  • Write the SHM position equation and read off amplitude, angular frequency, and phase.
  • Compute the angular frequency of a mass-spring system and of a simple pendulum.
  • Track the exchange between kinetic and potential energy across an oscillation cycle.

Formulas covered: SHM position equation · Angular frequency of a mass-spring oscillator · Angular frequency of a simple pendulum · Period from angular frequency · Total energy in SHM · Maximum speed in SHM

Read the Simple Harmonic Motion note

Gauss's Law and Electric Fields

A free GRE Physics electromagnetism note on Gauss's law, symmetry arguments for spheres, lines, and planes, conductor properties, and the field-potential relationship.

  • State Gauss's law and identify the charge enclosed by a chosen Gaussian surface.
  • Match spherical, cylindrical, and planar symmetry to the Gaussian surface that makes the flux integral trivial.
  • Use conductor properties: zero interior field, surface charge, and the field just outside a conductor.

Formulas covered: Gauss's law · Field outside a spherical charge distribution · Field of an infinite line charge · Field of an infinite charged plane · Field from potential (one dimension)

Read the Gauss's Law and Electric Fields note

DC Circuits

A free GRE Physics electromagnetism note on Ohm's law, series and parallel resistors, Kirchhoff's rules, and the RC charging and discharging time constant.

  • Apply Ohm's law to relate voltage, current, and resistance in a circuit element.
  • Reduce series and parallel resistor networks to an equivalent resistance.
  • Set up junction and loop equations for circuits that do not reduce to series and parallel blocks.

Formulas covered: Ohm's law · Series resistors · Parallel resistors · Electrical power · RC time constant · Capacitor discharge

Read the DC Circuits note

Quantum Mechanics Foundations

A free GRE Physics quantum mechanics note on wavefunctions and probability, infinite square well energies, the Heisenberg uncertainty principle, and photon and de Broglie wavelength relations.

  • Interpret $|\Psi|^2$ as a probability density and use normalization to fix a wavefunction's amplitude.
  • Compute infinite square well energy levels and photon energies for transitions between them.
  • Apply the Heisenberg uncertainty principle to estimate minimum momentum spreads and ground-state energies.

Formulas covered: Born probability rule · Infinite square well energies · Heisenberg uncertainty principle · Photon energy · De Broglie wavelength

Read the Quantum Mechanics Foundations note

Thermodynamics and Heat Engines

A free GRE Physics thermodynamics note on the first law, entropy and the second law, Carnot efficiency, and the standard ideal-gas processes.

  • Apply the first law with a consistent sign convention for heat and work.
  • Classify isothermal, isobaric, isochoric, and adiabatic ideal-gas processes and identify which term of the first law vanishes in each.
  • Compute heat engine efficiency from heats or from work, and the Carnot bound from reservoir temperatures.

Formulas covered: First law of thermodynamics · Ideal gas law · Heat engine efficiency · Carnot efficiency · Entropy change (reversible heat transfer) · Adiabatic ideal-gas relation

Read the Thermodynamics and Heat Engines note

Special Relativity Essentials

A free GRE Physics special relativity note on the two postulates, time dilation, length contraction, and the relativistic energy-momentum relation.

  • State the two postulates and explain why they force observers to disagree about time and length measurements.
  • Identify proper time and proper length, and apply the Lorentz factor in the correct direction.
  • Compute relativistic momentum and total energy, and use $E^2 = (pc)^2 + (mc^2)^2$ to relate them.

Formulas covered: Lorentz factor · Time dilation · Length contraction · Relativistic momentum · Energy-momentum relation

Read the Special Relativity Essentials note

Interference and Diffraction

A free GRE Physics optics note on double-slit interference, diffraction gratings, single-slit diffraction minima, and thin-film interference with phase shifts.

  • Locate double-slit and grating maxima with $d\sin\theta = m\lambda$ and convert to screen positions in the small-angle limit.
  • Locate single-slit minima with $a\sin\theta = m\lambda$ and explain why the central maximum is twice as wide as the others.
  • Account for the wavelength inside a film ($\lambda/n$) and reflection phase shifts in thin-film problems.

Formulas covered: Double-slit maxima · Fringe spacing (small angles) · Diffraction grating maxima · Single-slit minima · Thin-film constructive reflection (one phase shift)

Read the Interference and Diffraction note

Photons, Work Functions, and Matter Waves

A free GRE Physics note on the two quantization facts atomic-physics questions lean on: light delivers energy in photons of energy hf, and a particle of momentum p behaves like a wave of wavelength h/p.

  • Convert between photon wavelength, frequency, and energy using $E = hf = hc/\lambda$.
  • Apply $K_{\max} = hf - \phi$ and explain why intensity changes the emitted current but not $K_{\max}$.
  • Compute a de Broglie wavelength from momentum, including the nonrelativistic case $p = \sqrt{2mK}$.

Formulas covered: Photon energy · Photoelectric equation · De Broglie wavelength

Read the Photons, Work Functions, and Matter Waves note

Measurement Uncertainty and Error Analysis

A free GRE Physics laboratory-methods note on random versus systematic error, propagating uncertainty through sums and products, why averaging improves precision as one over the square root of N, and how real meters load the circuit they measure.

  • Classify an error as random or systematic and say which one repeating the measurement can fix.
  • Propagate uncertainty through a sum, a product, a quotient, and a power without mixing absolute and relative forms.
  • Use $\sigma/\sqrt{N}$ and $1/\sqrt{N}$ to predict how much averaging or counting longer actually buys.

Formulas covered: Percent uncertainty · Sum or difference: absolute uncertainties combine · Product, quotient, or power: relative uncertainties combine · Standard error of the mean · Counting statistics

Read the Measurement Uncertainty and Error Analysis note

Classical Mechanics Domain Guide

The whole GRE Physics mechanics domain in one place: forces and free-body diagrams, the conservation laws and when each one is legal, rotation and rolling, oscillations, orbits, and statics of fluids — with the traps that decide most items.

  • Choose between a force analysis, an energy analysis, and a momentum analysis from the wording of the question rather than by trial.
  • Draw a free-body diagram that shows only external forces on a clearly named system, and read the constraint (incline, pulley, contact) off the geometry.
  • Apply momentum conservation across collisions and energy conservation between configurations, and state out loud which one fails and why in an inelastic collision.

Formulas covered: Newton's second law and the constraint forces it determines · Work-energy theorem and mechanical energy · Collisions: momentum always, kinetic energy only if elastic · Rotation, rolling, and the parallel-axis theorem · Simple harmonic motion in every disguise · Damped and driven oscillation · Gravitation and orbits · Fluid statics and steady flow

Read the Classical Mechanics Domain Guide note

Electromagnetism Domain Guide

Electrostatics, circuits, magnetostatics, induction, and electromagnetic waves as one subject: the four Maxwell equations, the symmetry shortcuts that make them computable, and the sign conventions that decide most wrong answers.

  • Decide in one glance whether a field problem has spherical, cylindrical, or planar symmetry, and apply Gauss's law only when it does.
  • Move fluently between $\vec{E}$, $V$, and $U$, using the scalar potential whenever superposition would otherwise require vector addition.
  • Reduce any resistor network to one equivalent resistance, then walk back through it to recover branch currents and voltages, and apply Kirchhoff's rules when the network is not reducible.

Formulas covered: Gauss's law and its three standard results · Potential, field, and stored energy · Resistor and capacitor combinations, and power · Transients: what a capacitor and an inductor do at t = 0 and t = infinity · Magnetic fields of standard current geometries · Magnetic force and circular motion · Faraday's law, Lenz's law, and motional EMF · Electromagnetic waves

Read the Electromagnetism Domain Guide note

Quantum Mechanics Domain Guide

Wavefunctions, operators, and the three solvable systems the GRE Physics Test reuses: the infinite well, the harmonic oscillator, and hydrogen — plus superposition, measurement, uncertainty, and the scaling rules that answer most items without an integral.

  • Normalise a wavefunction and convert between $|\Psi|^{2}$, a probability over an interval, and an expectation value.
  • Read off the energy spectrum and its scaling for the infinite well ($E_n \propto n^{2}$), the harmonic oscillator ($E_n \propto n + \tfrac{1}{2}$), and hydrogen ($E_n \propto -1/n^{2}$).
  • Expand a state in energy eigenstates and give measurement probabilities, the expectation value of the energy, and the oscillation frequency of the resulting probability density.

Formulas covered: The Schrodinger equation and normalisation · The three solvable spectra and how each one scales · Superposition, measurement, and time evolution · Uncertainty relations · Barrier tunnelling · Angular momentum, spin, and degeneracy · Photons, matter waves, and the constant that saves the arithmetic

Read the Quantum Mechanics Domain Guide note

Thermodynamics Domain Guide

The laws, the ideal gas and its named processes, kinetic theory and equipartition, engines and the Carnot bound, entropy, calorimetry, and heat transfer — organised around the one question that unlocks most items: which variable is being held fixed?

  • Apply $\Delta U = Q - W$ with a stated sign convention and identify, for any named process, which of $Q$, $W$, $\Delta U$, or $\Delta T$ is zero.
  • Use $PV = nRT$ together with $PV^{\gamma} = \text{constant}$ and $TV^{\gamma-1} = \text{constant}$ to relate states across an adiabatic change.
  • Derive heat capacities from degrees of freedom: $C_V = \tfrac{3}{2}R$ and $\gamma = \tfrac{5}{3}$ for a monatomic gas, $C_V = \tfrac{5}{2}R$ and $\gamma = \tfrac{7}{5}$ for a rigid diatomic.

Formulas covered: First law and the four named processes · Ideal gas law and adiabatic relations · Kinetic theory and equipartition · Engines, refrigerators, and the Carnot bound · Entropy · Calorimetry and phase change · Heat transfer and thermal expansion

Read the Thermodynamics Domain Guide note

Optics and Waves Domain Guide

Travelling and standing waves, the Doppler effect and beats, reflection and refraction with sign conventions, and the interference and diffraction conditions that look alike and mean opposite things.

  • Relate speed, frequency, and wavelength across a boundary, and say which of the three is unchanged and why.
  • Compute the harmonic series of a string, an open pipe, and a closed pipe, and explain why the closed pipe has only odd harmonics.
  • Apply the Doppler formula for sound with the correct sign on source and observer motion, and compute beat frequencies.

Formulas covered: Wave speed in a medium · Standing waves and beats · Doppler effect · Refraction, total internal reflection, and the mirror/lens equation · Double slit, single slit, and grating · Thin-film interference · Polarisation and resolution

Read the Optics and Waves Domain Guide note

Atomic Physics Domain Guide

Atomic structure and spectra, X-rays and Bragg diffraction, solids and band structure, and nuclear binding and decay — the specialised block, unified by one constant and one habit: work in electronvolts and think in ratios.

  • Compute transition energies and photon wavelengths for hydrogen-like atoms and scale them correctly with $Z$ and $n$.
  • Apply the photoelectric relation, distinguish the effect of intensity from the effect of frequency, and find a stopping potential or threshold wavelength.
  • Assign quantum numbers, apply the Pauli exclusion principle, and count shell capacities and level degeneracies.

Formulas covered: Hydrogen-like atoms · Photons, the photoelectric effect, and the stopping potential · Quantum numbers, shell capacity, and selection rules · X-ray production and Bragg diffraction · Solids: bands, Fermi energy, and heat capacity · Nuclear binding, decay bookkeeping, and the exponential law

Read the Atomic Physics Domain Guide note

Special Relativity Domain Guide

Two postulates, one factor, and a strict discipline about whose clock and whose ruler: time dilation, length contraction, simultaneity, velocity addition, and relativistic energy and momentum.

  • Compute $\gamma$ and $\beta$ from each other and recognise when a problem is safely non-relativistic.
  • Identify the proper time and proper length in a scenario, then apply dilation and contraction in the correct direction.
  • Apply the Lorentz transformations to coordinates and use the $-vx/c^{2}$ term to explain a simultaneity disagreement.

Formulas covered: The Lorentz factor and its scale · Time dilation and length contraction · Lorentz transformations and the invariant interval · Relativistic velocity addition and Doppler shift · Relativistic energy and momentum · Conserved quantities in interactions

Read the Special Relativity Domain Guide note

Lab Methods Domain Guide

Uncertainty propagation, counting statistics, significant figures, and the instruments the exam expects you to reason about — the block where a candidate who has practised the rules can score close to full marks.

  • Classify an error as random or systematic and say whether repeating the measurement helps.
  • Propagate uncertainties through sums, differences, products, quotients, and powers using the quadrature rules.
  • Apply Poisson counting statistics, including background subtraction and its effect on the net uncertainty.

Formulas covered: Propagation of uncertainty · Counting statistics · Mean, standard deviation, and standard error · Significant figures and reporting · Linearising data for a straight-line fit · Meters and detectors

Read the Lab Methods Domain Guide note

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What these questions are built to catch

Every wrong answer in the GRE Physics bank was written to catch one specific mistake, and each is recorded by name. The taxonomy sets out the named mistakes for this exam, grouped by the part of the syllabus each turns up in, with what to do differently. It describes how the questions were written, not how students perform.

Open the GRE Physics section of the error taxonomy

Exam page sources

  1. GRE Subject Test Content and Structure — ETS. Accessed 2026-07-06. Use as a cited source for exam facts; do not imply affiliation or reproduce protected test material.
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