GRE · GRE Subject Test

GRE Physics

Papers, samples and curriculum documents for this course.

Course units and learning goals

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme.

Lessons →Vocabulary practice →

CM · Classical mechanics

Apply Newtonian, Lagrangian and Hamiltonian descriptions
Analyse rotation, central forces and oscillations
Use conservation laws with their conditions

Lagrangian: Kinetic energy minus potential energy for the standard mechanical system
angular momentum: The moment of linear momentum about a reference point

EM · Electromagnetism

Use electrostatic potentials, fields and Gauss’s law
Analyse circuits, magnetism and induction
Apply Maxwell equations and electromagnetic wave relationships

flux: The surface integral of a field’s normal component
potential: Potential energy per unit charge

WO · Waves and optics

Analyse wave superposition and interference
Use diffraction, polarisation and optical imaging
Relate phase, frequency and dispersion

coherence: A stable phase relationship between waves
diffraction: Wave spreading and interference caused by an aperture or obstacle

TS · Thermodynamics and statistical mechanics

Apply the first and second laws with a sign convention
Relate ensembles, Boltzmann factors and entropy
Analyse ideal gases, heat engines and quantum statistics

entropy: A state quantity connected to multiplicity and reversible heat transfer
partition function: The sum of statistical weights used to normalise probabilities

QM · Quantum mechanics and atomic physics

Use wavefunctions, operators and measurement probabilities
Solve standard bound-state models and tunnelling reasoning
Apply angular momentum, spin and atomic spectral principles

normalisation: Making total probability equal to one
operator: A mathematical action representing an observable

RA · Relativity, laboratory methods and specialised topics

Apply special-relativistic energy and spacetime relations
Propagate measurement uncertainty and analyse experimental data
Recognise nuclear, particle, condensed-matter and astrophysical concepts

precision: Closeness of repeated measurements to each other
covariance: A measure of joint variation used for correlated uncertainties

AT · Atomic spectra and selection rules

Relate atomic energies to spectral lines
Apply angular-momentum quantum numbers
Distinguish allowed and forbidden electric-dipole transitions

selection rule: A restriction on transitions for a specified interaction mechanism
Zeeman splitting: Magnetic-field splitting of atomic energy levels

SN · Solid-state, nuclear and particle models

Use band and carrier descriptions
Apply radioactive decay and binding-energy ideas
Check conservation laws in particle reactions

band gap: An energy interval with no allowed bulk electronic states in the band model
half-life: Time for a radioactive population to halve

AH · Hamiltonian mechanics and astrophysical scaling

Construct a simple Hamiltonian
Use canonical equations
Apply gravitational and radiative scaling

canonical momentum: The derivative of the Lagrangian with respect to a generalised velocity
luminosity: Total emitted power, distinct from flux at an observer

CM.1 · Collisions, work and oscillator energy

Compute vector momentum and energy loss in sticking collisions
Compare fixed-force springs and use work–energy conditions
Derive small-oscillation periods and oscillator energies

external impulse: Time integral of the net force from outside the chosen system
turning point: An extreme oscillator position where its instantaneous speed is zero

CM.2 · Rotation, buoyancy and terminal-speed balances

Use pivot torque and rotational inertia consistently
Partition rolling kinetic energy with the no-slip constraint
Balance buoyancy and drag for composite bodies

moment of inertia: Mass-weighted squared perpendicular distance from a specified rotation axis
terminal speed: Steady speed at which opposing forces balance

CM.3 · Coupled acceleration and relative motion

Solve coupled-body equations using one acceleration constraint
Transform velocities between inertial frames
Check force and energy limits for constrained motion

constraint: A condition linking allowed positions or motions of connected bodies
relative velocity: Velocity of one object measured in another moving frame

EM.1 · Electrostatic superposition, flux and conductors

Add Coulomb forces as vectors using the actual geometry
Compute flux from symmetry or solid angle with a stated orientation
Find conductor fields and potentials using induced surface charges

solid angle: Angular area subtended by a surface, measured in steradians
induced surface charge: Charge rearranged on a conductor to satisfy electrostatic equilibrium

EM.2 · Circuit power, induction and charged-particle motion

Solve resistor networks and distinguish rms from peak AC quantities
Apply flux linkage, Lenz direction and the current-loop field
Use charge-to-mass ratios and balance crossed-field forces

root mean square: Square root of the mean squared value, used for effective AC current or voltage
flux linkage: Sum of magnetic flux through a coil’s turns

EM.3 · Maxwell waves, energy flow and boundary conditions

Use displacement current and material wave-speed relations
Determine wave-field directions and radiated energy flow
Apply Maxwell boundary conditions without confusing field components

displacement current: Electric-flux time-derivative contribution in Ampere–Maxwell law
Poynting vector: Electromagnetic energy flux per unit area and time

WO.1 · Acoustic Doppler echoes and standing-wave boundaries

Apply source and observer Doppler factors in the medium frame
Derive allowed pipe frequencies from displacement boundary conditions
Distinguish frequency, wavelength and boundary changes

displacement antinode: A standing-wave position where the air displacement amplitude is maximal
Doppler factor: Frequency multiplier produced by a specified source or observer motion

WO.2 · Optical instruments, path differences and refraction

Calculate telescope magnification and grating resolving power
Relate Michelson fringe counts to double-pass optical path changes
Trace surface normals before applying Snell and reflection laws

resolving power: Wavelength divided by the smallest resolvable wavelength separation
optical path length: Geometric path weighted by refractive index along the ray

WO.3 · Fourier symmetry and wave superposition

Use orthogonality to identify Fourier coefficients
Exploit even and odd parity without discarding the constant term
Relate component amplitudes to interference and physical waveforms

orthogonality: A zero integral of the product of distinct basis functions over the specified interval
Fourier coefficient: Weight of a sine, cosine or constant basis component in a periodic expansion

TS.1 · Gas processes, entropy and reversible cycles

Apply first-law work and heat signs to gas processes
Compare reversible entropy balances and P–V cycle areas
Distinguish engine efficiency from refrigerator coefficient of performance

entropy production: Nonnegative total entropy generated by irreversibility
coefficient of performance: Useful heat transferred divided by work input for a refrigerator or heat pump

TS.2 · Speed distributions and statistical ensembles

Normalise continuous speed densities and interpret their units
Distinguish vector means, speed means and most probable speeds
Use Boltzmann weights with degeneracy and a partition function

probability density: Probability per unit of a continuous variable, whose integral gives interval probability
partition function: Sum of statistical weights used to normalise equilibrium state probabilities

LM.1 · Counting statistics, uncertainty and dimensional models

Use binomial and Poisson count means and fluctuations
Propagate small uncertainties with stated correlation assumptions
Solve dimensional exponent constraints and check a model’s units

standard uncertainty: Uncertainty expressed as a standard deviation under a stated measurement model
Poisson approximation: Rare independent-event count model with variance equal to its mean

RA.1 · Relativistic lifetime, energy and Doppler shift

Relate proper lifetime to laboratory time and distance
Use invariant energy–momentum and relativistic kinetic energy
Infer longitudinal recession speed from wavelength ratio

proper time: Time recorded by a clock moving with the object along its worldline
rest energy: Energy mc² associated with an object’s rest mass

AT.1 · Photoelectrons, reduced mass and atomic excitation

Distinguish photoelectric thresholds and characteristic X rays
Apply reduced-mass spectral scaling and many-electron spin filling
Interpret Franck–Hertz energy spacing without inventing new levels

work function: Minimum energy required to remove an electron from the specified surface
reduced mass: Two-body effective mass m1m2/(m1+m2) for relative motion

QM.1 · Scattering, degeneracy and Pauli operators

Match travelling waves and fluxes across finite potential changes
Count degenerate isotropic-oscillator states
Evaluate Pauli products and distinguish anticommutation from equality

reflection coefficient: Reflected probability-current fraction relative to incident current
degeneracy: Number of independent states sharing the specified energy

SN.1 · Nuclear binding, particle families and Hall carriers

Compare binding energy per nucleon and reaction energy
Distinguish leptons, mesons and baryons with conservation constraints
Infer dominant carrier sign from the one-carrier Hall model

binding energy per nucleon: Nuclear binding energy divided by nucleon count
Hall coefficient: Signed proportionality relating transverse Hall field to current density and magnetic field under a stated convention

CM.4 · Constraints, variational equations and cyclic coordinates

Derive Euler–Lagrange motion after imposing a holonomic constraint
Use a cyclic coordinate to identify conserved canonical momentum
Linearise a stable equilibrium and check the resulting frequency

holonomic constraint: A constraint expressible as a relation among coordinates and possibly time
cyclic coordinate: A coordinate absent explicitly from the Lagrangian, with conserved canonical momentum under the Euler–Lagrange equation

CM.5 · Accelerating and rotating reference frames

Transform acceleration with translating and rotating frame terms
Determine centrifugal, Coriolis and Euler directions from cross products
Separate apparent forces from real interactions and test inertial limits

Coriolis force: The apparent rotating-frame force −2mΩ×v′ caused by relative motion
centrifugal force: The apparent rotating-frame force −mΩ×(Ω×r), directed away from the rotation axis

CM.6 · Fluid continuity, pressure energy and viscous flow

Combine incompressible continuity with pressure, height and kinetic energy
Apply hydrostatic and Bernoulli relations only under their stated conditions
Use viscosity, Poiseuille scaling and Reynolds number to distinguish flow regimes

volume flow rate: Volume crossing a section per unit time, Q=Av for mean speed v
dynamic viscosity: The coefficient relating shear stress to velocity gradient in a Newtonian fluid

EM.4 · Polarisation, magnetisation and material fields

Relate free and bound charge to D, E and polarisation
Compare fixed-charge and fixed-voltage dielectric changes
Use magnetic constitutive response and free-current boundary conditions

electric polarisation: Electric dipole moment per unit volume, P, contributing bound charge
magnetisation: Magnetic dipole moment per unit volume, M, entering B=μ₀(H+M)

EM.5 · RC and RL transients, impedance and resonance

Solve RC charging and discharging with stated initial conditions
Solve RL current response and account for stored energy
Use complex impedance, phase and resonance in sinusoidal circuits

time constant: The exponential response scale, RC for an RC circuit and L/R for an RL circuit
impedance: The complex voltage-to-current phasor ratio in sinusoidal steady state

WO.4 · Polarisation, analyser chains and phase

Calculate successive ideal analyser transmissions from the immediate input state
Distinguish linear, circular and elliptical field motion using relative phase
Use Brewster incidence with refractive-index and plane-of-incidence conventions

Malus’s law: Ideal linear-analyser intensity law I_out=I_in cos²θ for linearly polarised input
Brewster angle: Incidence angle at which the reflected p component vanishes for the ideal dielectric interface

WO.5 · Diffraction envelopes and missing interference orders

Derive and evaluate the far-field single-slit intensity using amplitude superposition
Separate double-slit interference spacing from finite-aperture envelope width
Identify missing orders and state the limits of far-field and small-angle formulas

diffraction envelope: The aperture-dependent intensity factor that modulates the interference pattern
missing order: An interference order cancelled because it coincides with an aperture intensity zero

WO.6 · Signed lens and mirror images

Locate paraxial thin-lens and spherical-mirror images with a declared sign convention
Use signed magnification to classify orientation and real or virtual character
Track successive image locations as the next element’s object without resetting geometry

virtual image: An apparent image located by backwards ray extensions rather than actual outgoing-ray convergence
transverse magnification: Signed image-height to object-height ratio, −s′/s in the declared convention

TS.3 · Thermal transport, calorimetry and expansion

Combine conductive thermal resistances and distinguish heat rate from heat flux
Balance sensible and latent heat with stated isolation and heat-capacity conditions
Calculate free thermal expansion and constrained thermal stress with their limits

thermal resistance: Temperature difference per steady heat-transfer rate, measured in K/W
latent heat: Energy transferred during a phase change at its transition temperature; specific latent heat is per mass

TS.4 · Partition derivatives, energy fluctuations and heat capacity

Obtain canonical mean energy and free energy from a fixed energy spectrum
Relate energy variance to constant-volume heat capacity with fixed-spectrum conditions
Evaluate entropy and low/high-temperature limits for an original finite-level model

energy fluctuation: Canonical spread of energy about its ensemble mean, quantified by the energy variance
Helmholtz free energy: Thermodynamic potential F=U−TS, equal to −kBT lnZ for the canonical ensemble

TS.5 · Quantum occupations and limits of equipartition

Compute mean occupation per complete quantum state for fermions and bosons
Count allowed identical-particle occupations and identify the classical dilute limit
Compare classical quadratic-mode heat capacity with a quantum oscillator response

mean occupation: Ensemble average number of particles in one complete quantum state or a specified group of states
equipartition: Classical equilibrium rule assigning kBT/2 to each independent quadratic Hamiltonian term

QM.2 · Weak perturbations and degenerate subspaces

Calculate nondegenerate first-order energy shifts as normalised expectation values
Use symmetry and matrix elements to assess weak-coupling limits
Diagonalise the perturbation within an exactly degenerate subspace

first-order energy shift: Leading weak-perturbation correction given by the unperturbed state’s expectation value
degenerate perturbation theory: Method that first diagonalises the perturbation within an unperturbed degenerate subspace

QM.3 · Exchange symmetry, spin pairs and Pauli exclusion

Construct normalised symmetric and antisymmetric two-orbital spatial states
Combine spatial and spin symmetry to produce allowed two-electron states
Count complete-state occupations and interpret exchange-induced correlations

spin singlet: Antisymmetric two-spin-1/2 state with total spin S=0
Slater determinant: Antisymmetric fermionic construction from complete single-particle states; duplicate states make it vanish

QM.4 · Finite-well bound states and hydrogenic quantum numbers

Match decaying finite-well states and derive parity-dependent quantisation conditions
Interpret dimensionless bound-state roots and distinguish confinement from scattering
Use hydrogenic quantum numbers, angular momentum and radial probability measures

bound state: Normalisable stationary state with confined probability and discrete energy in the specified model
radial probability density: Probability per radial distance, including the spherical-shell measure after angular integration

AT.2 · Atomic field shifts and spectral differences

Calculate orbital and spin magnetic shifts in the appropriate coupling regime
Find photon-energy shifts from allowed upper-minus-lower level changes
Contrast parity cancellation with degenerate electric-field splitting

Landé factor: Projection factor relating a weak-field LS-coupled magnetic shift to g_J m_J
Stark splitting: Electric-field-induced separation of atomic energy levels, with symmetry and degeneracy controlling leading order

AT.3 · Thermal spectra and one-electron scaling

Distinguish wavelength spectral peak, integrated radiation and photon energy
Derive Bohr radius and energy scaling under one-electron assumptions
Calculate Coulomb-ion transitions, series limits and ionisation thresholds

spectral radiance: Radiation intensity per projected area, solid angle and stated spectral interval
series limit: Limiting bound-bound photon energy or wavelength as the initial level approaches the continuum for a fixed final level

Preparing for this qualification

Approximately 70 multiple-choice items in 120 minutes. Mechanics, electromagnetism, optics/waves, thermal/statistical physics, quantum/atomic physics, relativity, laboratory methods and specialised topics. No A-level equivalence is claimed.

Teaching coverage still needed

The complete official sample has reviewed questions, diagrams, answer keys and teaching targets. The 41 preparation units provide 123 local objectives, including variational mechanics, rotating frames, fluid flow, material fields, circuit transients, polarisation, diffraction, signed image formation, thermal transport, partition derivatives, quantum occupations, perturbation, exchange symmetry, bound states, atomic-field shifts and radiative spectra. Further depth is required across six areas, including spacetime transformations, laboratory instruments and solid-state/nuclear models. Complete original timed practice and on-screen official-paper practice remain unfinished. A complete sample-paper target map does not establish exhaustive undergraduate scope.