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Give the Euler–Lagrange equation and what L stands for. \(\dfrac{d}{dt}\dfrac{\
partial L}{\partial \dot q} - \dfrac{\partial L}{\partial q} = 0\), where \(L = T -
V\). GRE_Physics::Mechanics
Give Hamilton's equations. \(\dot q = \partial H/\partial p\), \(\dot p = -\
partial H/\partial q\), with \(H = T+V\). GRE_Physics::Mechanics
Give the angular frequency of a simple harmonic oscillator.\(\omega = \sqrt{k/m}\).
GRE_Physics::Mechanics
When is angular momentum conserved? Whenever the net external torque on the system
is zero. GRE_Physics::Mechanics
State Kepler's third law. \(T^2 \propto a^3\) — orbital period squared is
proportional to the semi-major axis cubed. GRE_Physics::Mechanics
What's the key difference between a Lagrangian and a Hamiltonian approach?
Lagrangian mechanics uses position and velocity (\(q,\dot q\)); Hamiltonian
mechanics uses position and momentum (\(q,p\)), and treats energy as the central
quantity. GRE_Physics::Mechanics
List Maxwell's four equations by name. Gauss's law, Gauss's law for magnetism,
Faraday's law, Ampère–Maxwell law. GRE_Physics::EandM
Give Coulomb's law in vector form. \(\vec F = \dfrac{1}{4\pi\varepsilon_0}\
dfrac{q_1q_2}{r^2}\hat r\). GRE_Physics::EandM
State Gauss's law in integral form. \(\oint \vec E \cdot d\vec A = Q_{\text{enc}}/\
varepsilon_0\). GRE_Physics::EandM
Give the speed of light in terms of the EM constants. \(c = 1/\sqrt{\mu_0\
varepsilon_0}\). GRE_Physics::EandM
What does the Poynting vector represent? The directional energy flux (power per
unit area) carried by an electromagnetic wave: \(\vec S = \vec E \times \vec B / \
mu_0\). GRE_Physics::EandM
Roughly what fraction of GRE E&M questions are conceptual rather than
computational? About half — field direction, symmetry, and boundary-condition
reasoning show up as often as calculation. GRE_Physics::EandM
State Snell's law. \(n_1\sin\theta_1 = n_2\sin\theta_2\).
GRE_Physics::Optics
Give the diffraction grating equation for bright fringes. \(d\sin\theta = m\
lambda\). GRE_Physics::Optics
State Malus's law. \(I = I_0\cos^2\theta\), for light through a polarizer at
angle θ to the incoming polarization. GRE_Physics::Optics
What extra phase shift do you need to track in thin-film interference? A half-
wavelength (π) phase shift occurs on reflection from a higher-index medium — the
most common trap in these problems. GRE_Physics::Optics
Give the Rayleigh criterion for angular resolution. \(\theta_{\min} \approx
1.22\,\lambda/D\), where D is the aperture diameter. GRE_Physics::Optics
What weight does Optics & Wave Phenomena carry on the GRE Physics exam? About
8% of the test. GRE_Physics::Optics
State the ideal gas law. \(PV = nRT\). GRE_Physics::Thermo
Give the Boltzmann factor. \(P(E_i) \propto e^{-E_i/k_BT}\) — the relative
probability of a state at energy \(E_i\). GRE_Physics::Thermo
Define the partition function. \(Z = \sum_i e^{-E_i/k_BT}\), the normalizing
sum over all accessible states. GRE_Physics::Thermo
Give the statistical definition of entropy. \(S = k_B \ln \Omega\), where Ω is
the number of accessible microstates. GRE_Physics::Thermo
Why is stat mech worth extra review time relative to its 10% weight? It's usually
taught last in the undergraduate sequence, so it's the most under-reviewed topic
relative to how testable it is. GRE_Physics::Thermo
Most stat-mech GRE questions reduce to which two quantities? The Boltzmann
factor and the partition function. GRE_Physics::Thermo
Write the time-dependent Schrödinger equation. \(i\hbar\,\partial \Psi/\partial t
= \hat H \Psi\). GRE_Physics::Quantum
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#tags column:3
Give the Euler–Lagrange equation and what L stands for. \(\dfrac{d}{dt}\dfrac{\
partial L}{\partial \dot q} - \dfrac{\partial L}{\partial q} = 0\), where \(L = T -
V\). GRE_Physics::Mechanics
Give Hamilton's equations. \(\dot q = \partial H/\partial p\), \(\dot p = -\
partial H/\partial q\), with \(H = T+V\). GRE_Physics::Mechanics
Give the angular frequency of a simple harmonic oscillator.\(\omega = \sqrt{k/m}\).
GRE_Physics::Mechanics
When is angular momentum conserved? Whenever the net external torque on the system
is zero. GRE_Physics::Mechanics
State Kepler's third law. \(T^2 \propto a^3\) — orbital period squared is
proportional to the semi-major axis cubed. GRE_Physics::Mechanics
What's the key difference between a Lagrangian and a Hamiltonian approach?
Lagrangian mechanics uses position and velocity (\(q,\dot q\)); Hamiltonian
mechanics uses position and momentum (\(q,p\)), and treats energy as the central
quantity. GRE_Physics::Mechanics
List Maxwell's four equations by name. Gauss's law, Gauss's law for magnetism,
Faraday's law, Ampère–Maxwell law. GRE_Physics::EandM
Give Coulomb's law in vector form. \(\vec F = \dfrac{1}{4\pi\varepsilon_0}\
dfrac{q_1q_2}{r^2}\hat r\). GRE_Physics::EandM
State Gauss's law in integral form. \(\oint \vec E \cdot d\vec A = Q_{\text{enc}}/\
varepsilon_0\). GRE_Physics::EandM
Give the speed of light in terms of the EM constants. \(c = 1/\sqrt{\mu_0\
varepsilon_0}\). GRE_Physics::EandM
What does the Poynting vector represent? The directional energy flux (power per
unit area) carried by an electromagnetic wave: \(\vec S = \vec E \times \vec B / \
mu_0\). GRE_Physics::EandM
Roughly what fraction of GRE E&M questions are conceptual rather than
computational? About half — field direction, symmetry, and boundary-condition
reasoning show up as often as calculation. GRE_Physics::EandM
State Snell's law. \(n_1\sin\theta_1 = n_2\sin\theta_2\).
GRE_Physics::Optics
Give the diffraction grating equation for bright fringes. \(d\sin\theta = m\
lambda\). GRE_Physics::Optics
State Malus's law. \(I = I_0\cos^2\theta\), for light through a polarizer at
angle θ to the incoming polarization. GRE_Physics::Optics
What extra phase shift do you need to track in thin-film interference? A half-
wavelength (π) phase shift occurs on reflection from a higher-index medium — the
most common trap in these problems. GRE_Physics::Optics
Give the Rayleigh criterion for angular resolution. \(\theta_{\min} \approx
1.22\,\lambda/D\), where D is the aperture diameter. GRE_Physics::Optics
What weight does Optics & Wave Phenomena carry on the GRE Physics exam? About
8% of the test. GRE_Physics::Optics
State the ideal gas law. \(PV = nRT\). GRE_Physics::Thermo
Give the Boltzmann factor. \(P(E_i) \propto e^{-E_i/k_BT}\) — the relative
probability of a state at energy \(E_i\). GRE_Physics::Thermo
Define the partition function. \(Z = \sum_i e^{-E_i/k_BT}\), the normalizing
sum over all accessible states. GRE_Physics::Thermo
Give the statistical definition of entropy. \(S = k_B \ln \Omega\), where Ω is
the number of accessible microstates. GRE_Physics::Thermo
Why is stat mech worth extra review time relative to its 10% weight? It's usually
taught last in the undergraduate sequence, so it's the most under-reviewed topic
relative to how testable it is. GRE_Physics::Thermo
Most stat-mech GRE questions reduce to which two quantities? The Boltzmann
factor and the partition function. GRE_Physics::Thermo
Write the time-dependent Schrödinger equation. \(i\hbar\,\partial \Psi/\partial t
= \hat H \Psi\). GRE_Physics::Quantum
