APS Graduate Exam flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Dimensional analysis

A method checking physical equations by requiring identical mass, length, and time exponents on both sides; also used to derive the form of unknown relations up to a dimensionless constant.

de Broglie wavelength

The wavelength associated with a particle of momentum p, given by λ = h/p; it explains electron diffraction and sets the scale at which quantum effects become important.

Carnot efficiency

The maximum efficiency of a heat engine operating reversibly between hot and cold reservoirs, η = 1 − T_c/T_h; it depends only on the reservoir temperatures, not the working substance.

Gauss's law

The electric flux through a closed surface equals the enclosed charge divided by ε0; symmetry lets it yield the field of spheres, cylinders, and infinite planes.

Parallel-axis theorem

Relates moments of inertia about a body's center of mass and a parallel axis: I = I_cm + Md², where d is the perpendicular distance between the two axes.

Heisenberg uncertainty principle

States that Δx Δp ≥ ħ/2 for position and momentum; the spreads are intrinsic statistical properties of the state, not artifacts of clumsy measurement.

Photoelectric effect

Light above a threshold frequency ejects electrons with maximum kinetic energy hf − φ; intensity controls the count, not the energy, of emitted electrons.

Entropy as state function

For a reversible path dS = δQ/T; entropy depends only on the state, so its change between two states is path-independent even for irreversible processes.

Faraday's law of induction

A changing magnetic flux through a loop induces an EMF equal to −dΦ_B/dt; the minus sign reflects Lenz's law opposing the change.

Simple harmonic oscillator

A system obeying ẍ = −ω²x, giving sinusoidal motion at angular frequency ω; examples include springs, small pendulums, and LC circuits near equilibrium.

Partition function

The sum Z = Σ exp(−E_i/k_B T) over states; it encodes the statistical weights and yields thermodynamic quantities such as free energy F = −k_B T ln Z.

Snell's law

Relates angles of incidence and refraction at an interface: n1 sin θ1 = n2 sin θ2; it follows from requiring the wave phase to match along the boundary.

Euler–Lagrange equations

Equations d/dt(∂L/∂q̇) − ∂L/∂q = 0 derived from a Lagrangian L = T − U; they produce the equations of motion for generalized coordinates.

Lorentz force law

The force on a charge in fields, F = q(E + v×B); the magnetic part is perpendicular to velocity and therefore does no work.

Infinite square well energies

A particle confined to a box of width L has energies E_n = n²π²ħ²/(2mL²); quantization arises from boundary conditions on the wavefunction.

Second law of thermodynamics

The total entropy of an isolated system never decreases; equality holds for reversible processes, and irreversible ones increase total entropy.

Fourier transform scaling

A function narrow in time has a broad frequency spectrum and vice versa; this reciprocal width relation underlies the time-bandwidth limit.

Kepler's third law

For orbits under gravity, T² = 4π²a³/(G(M+m)); the period squared is proportional to the semimajor axis cubed for a given central mass.

Capacitance and stored energy

Capacitance C = Q/V; a charged capacitor stores energy U = ½CV² = Q²/(2C), and inserting a dielectric of constant κ multiplies C by κ.

Equipartition theorem

In classical thermal equilibrium each quadratic degree of freedom carries average energy ½k_B T; it predicts heat capacities of gases and solids.

Uncertainty propagation in quadrature

For independent random errors, fractional uncertainties combine as squares added under a square root; e.g., for z = x^a y^b, add a²(σ_x/x)² and b²(σ_y/y)².

Standard error of the mean

For N independent measurements with standard deviation σ, the mean has uncertainty σ/√N; averaging reduces random scatter but not systematic bias.

Angular momentum conservation

When net external torque is zero, L = Iω is constant; a body reducing its moment of inertia spins faster, as with a skater pulling in their arms.

Maxwell's displacement current

Adding ε0 dΦ_E/dt to Ampère's law makes it consistent with charge conservation and lets Maxwell's equations predict electromagnetic waves traveling at c.

Stationary states

Solutions of Ĥψ = Eψ with definite energy; their probability density |ψ|² is time-independent, though the wavefunction carries a phase factor e^(−iEt/ħ).

Pauli exclusion principle

No two identical fermions can occupy the same quantum state; it follows from antisymmetry of the wavefunction and underlies electron shell structure.

Taylor series expansion

Expands a smooth function about a point using its derivatives: f(a) + f'(a)(x−a) + ½f''(a)(x−a)² + …; truncating it gives small-parameter approximations.

Hermitian operators

Operators equal to their own adjoint; they have real eigenvalues and orthogonal eigenfunctions, so they represent observable quantities in quantum mechanics.

Doppler shift

The change in observed frequency when source or observer moves; for sound f' = f(v ± v_o)/(v ∓ v_s), with signs set by approach or recession.

Clausius–Clapeyron relation

Gives the slope of a phase boundary, dP/dT = L/(TΔv), where L is latent heat and Δv the volume change between phases.

Work–energy theorem

The net work done on a particle equals its change in kinetic energy, W_net = ΔK; for conservative forces this connects to a potential energy function.

Total internal reflection

Occurs when light in a denser medium strikes an interface beyond the critical angle θ_c = arcsin(n2/n1); beyond it no refracted ray propagates.