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419

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20

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24

units

652

lectures

PU-101 · Newtonian Mechanics 18

D-021	Galilean Invariance of Newton's Laws force · symmetry
D-022	The Work-Energy Theorem force · energy
D-023	Conservative Forces and Potential Energy force · energy · fields
D-024	Conservation of Mechanical Energy energy · symmetry
D-025	Momentum Conservation from Newton's Third Law force · symmetry
D-026	The Center-of-Mass Theorem force · matter
D-027	Angular Momentum, Torque, and Central Forces force · symmetry
D-028	The Two-Body Problem and Reduced Mass force · matter
D-029	Effective Potential and the Orbit Equation force · energy · fields
D-030	Kepler's Three Laws from Gravity force · fields · symmetry
D-031	Small Oscillations and Simple Harmonic Motion force · energy · waves
D-032	Damped, Driven Oscillators and Resonance force · energy · waves
D-033	Coupled Oscillators and Normal Modes waves · energy · symmetry
D-034	The Tsiolkovsky Rocket Equation force · matter
D-035	The Moment-of-Inertia Tensor matter · symmetry
D-036	Euler's Equations and Torque-Free Precession force · matter · symmetry
D-037	Rotating Frames: Centrifugal and Coriolis Forces force · symmetry
D-038	Euler-Lagrange Equations from d'Alembert force · energy · symmetry

PU-102 · Electricity & Magnetism I 18

D-039	Electric Field from Coulomb's Law force · fields
D-040	Gauss's Law (Integral Form) from Coulomb fields · symmetry
D-041	Differential Gauss's Law via the Divergence Theorem fields · symmetry
D-042	Irrotationality of the Electrostatic Field fields · energy · symmetry
D-043	Scalar Potential, Poisson and Laplace Equations fields · energy
D-044	Uniqueness Theorem for Boundary-Value Problems fields · symmetry
D-045	Electrostatic Energy and Field Energy Density energy · fields
D-046	Fields at Conductor Surfaces fields · matter
D-047	Multipole Expansion of the Potential fields · symmetry
D-048	Dielectrics, Bound Charge and the D Field fields · matter
D-049	Continuity Equation and Charge Conservation matter · symmetry
D-050	Biot–Savart Law from the Current Force Law force · fields
D-051	Absence of Magnetic Monopoles fields · symmetry
D-052	Ampère's Circuital Law from Biot–Savart fields · symmetry
D-053	Magnetic Vector Potential and Gauge Freedom fields · symmetry
D-054	Magnetic Dipole: Field, Torque and Energy force · energy · fields
D-055	Lorentz Force and Cyclotron Motion force · fields
D-056	Magnetized Matter, Bound Currents and H fields · matter

PU-103 · Vibrations & Waves 18

D-057	Simple Harmonic Motion from a Linear Restoring Force force · energy
D-058	Energy Exchange and Conservation in SHM energy
D-059	The Damped Harmonic Oscillator force · energy
D-060	Quality Factor and Exponential Energy Decay energy
D-061	Driven Oscillator: Amplitude, Phase and Resonance force · energy
D-062	Power Absorption and the Lorentzian Lineshape energy
D-033	Coupled Oscillators and Normal Modes waves · energy · symmetry
D-063	Normal Coordinates for N Coupled Oscillators symmetry · energy
D-064	The Wave Equation as a Continuum Limit waves · force · symmetry
D-065	d'Alembert's General Solution waves
D-066	Standing Waves and Boundary Quantization waves · symmetry
D-067	Fourier Decomposition into Normal Modes waves · symmetry
D-068	Energy Density and Power Transport energy · waves
D-069	Reflection, Transmission and Impedance Matching waves · energy
D-070	Longitudinal Sound Waves in a Fluid waves · matter · energy
D-071	Dispersion, Phase Velocity and Group Velocity waves
D-072	Wave Packets, Group Velocity and Spreading waves
D-073	The Doppler Effect and Shock Fronts waves · matter

PU-104 · Mathematical Methods I — Linear Algebra & Operators 17

D-074	Invariance of Dimension of a Vector Space symmetry
D-075	Gram–Schmidt Orthonormalization symmetry · waves
D-076	Cauchy–Schwarz and the Triangle Inequality symmetry
D-077	Existence and Uniqueness of the Adjoint symmetry
D-078	Riesz Representation in Finite Dimensions symmetry
D-018	Properties of Hermitian Operators symmetry · matter · chance	verified
D-079	Determinant as the Unique Alternating Multilinear Form symmetry
D-080	Eigenvalues as Roots of the Characteristic Polynomial symmetry
D-081	Diagonalizability and the Eigenbasis Criterion symmetry
D-082	Spectral Theorem for Self-Adjoint Operators symmetry · matter · chance
D-083	Unitary Operators as Inner-Product Isometries symmetry
D-084	Simultaneous Diagonalization of Commuting Operators symmetry · matter
D-085	Normal Modes from the Generalized Eigenvalue Problem waves · symmetry · energy
D-086	Variational Characterization of Eigenvalues symmetry · energy
D-087	Singular Value Decomposition symmetry
D-088	Matrix Exponential and One-Parameter Flows symmetry · waves
D-089	Orthogonal Projections and Spectral Resolution symmetry · chance

PU-105 · Special Relativity 18

D-090	Lorentz Transformation from the Two Postulates light · symmetry
D-091	Invariance of the Spacetime Interval light · symmetry
D-092	Relativity of Simultaneity light · symmetry
D-093	Time Dilation light · symmetry
D-094	Length Contraction symmetry
D-095	Relativistic Velocity Addition light · symmetry
D-096	Rapidity and the Additivity of Boosts symmetry
D-097	Proper Time and the Four-Velocity symmetry · matter
D-098	Relativistic Momentum from Conservation matter · force · symmetry
D-099	Mass-Energy Equivalence E = mc^2 energy · matter · symmetry
D-100	The Energy-Momentum Four-Vector energy · matter · symmetry
D-101	Relativistic Doppler Effect and Aberration light · waves · symmetry
D-102	The Four-Wavevector and Phase Invariance light · waves · symmetry
D-103	Relativistic Force and Four-Acceleration force · matter · symmetry
D-104	The Electromagnetic Field Tensor fields · light · symmetry
D-105	Transformation of Electric and Magnetic Fields fields · symmetry
D-106	Covariant Form of Maxwell's Equations fields · light · symmetry
D-107	The Four-Current and Charge Conservation fields · symmetry

PU-106 · Experimental Physics & Data Analysis I 17

D-108	Expectation, Variance and Their Algebra chance
D-109	Variance of Linear Combinations and Covariance chance
D-110	First-Order Propagation of Uncertainty chance
D-111	Propagation with the Covariance Matrix chance
D-112	The Standard Error of the Mean chance
D-113	Bessel's Correction for Sample Variance chance
D-114	The Inverse-Variance Weighted Mean chance
D-115	The Binomial Distribution from Bernoulli Trials chance
D-116	Poisson Statistics of Counting chance
D-117	Characteristic Functions and Moments chance
D-118	The Central Limit Theorem chance
D-119	The Method of Maximum Likelihood chance
D-120	Least Squares from Gaussian Likelihood chance
D-121	Linear Least Squares and the Normal Equations chance
D-122	Parameter Uncertainties and the Cramer-Rao Bound chance
D-123	The Chi-Squared Distribution chance
D-124	Goodness of Fit and Degrees of Freedom chance

PU-201 · Analytical Mechanics 18

D-125	D'Alembert's Principle and Generalized Forces force · energy
D-001	The Euler-Lagrange Equation force · energy · symmetry	verified
D-126	Recovery of Newton's Second Law from L = T - V force · energy
D-127	Constraint Forces via Lagrange Multipliers force
D-002	Noether's Theorem for Time Translation energy · symmetry	verified
D-128	Noether's Theorem for Continuous Symmetries symmetry · energy · force
D-129	Cyclic Coordinates and Conserved Conjugate Momenta symmetry · energy
D-006	The Central-Force Orbit Equation force · energy · symmetry	verified
D-130	Effective Potential and Radial Reduction force · energy
D-131	Kepler Orbits and the Laplace-Runge-Lenz Vector force · symmetry · energy
D-003	Normal Modes as a Generalized Eigenproblem waves · energy · matter	verified
D-132	Decoupling into Normal Coordinates waves · energy
D-004	The Legendre Transform to the Hamiltonian energy · symmetry	verified
D-133	Hamilton's Canonical Equations energy · force · symmetry
D-005	Poisson Brackets and the Algebra of Observables energy · symmetry	verified
D-134	Liouville's Theorem on Phase-Space Volume energy · chance · symmetry
D-135	Canonical Transformations and Generating Functions symmetry · energy
D-136	The Hamilton-Jacobi Equation energy · waves · symmetry

PU-202 · Quantum Mechanics I 18

D-137	The Time-Dependent Schrödinger Equation matter · waves · energy
D-138	Born Rule and Conservation of Normalisation chance · matter · waves
D-007	Probability Current and the Continuity Equation chance · waves · matter	verified
D-139	Separation of Variables and Stationary States energy · waves · matter
D-140	Hermitian Operators: Real Eigenvalues and Orthogonal Eigenstates chance · symmetry
D-141	Expectation Values and the Operator Dictionary chance · matter · waves
D-142	The Canonical Commutator [x,p] = i hbar symmetry · matter
D-009	The Generalised Uncertainty Relation chance · symmetry · waves	verified
D-008	Ehrenfest's Theorem and the Classical Limit energy · matter · symmetry	verified
D-143	Bound States of the Infinite Square Well energy · waves · matter
D-144	Finite Square Well: Transcendental Quantisation energy · waves · matter
D-145	Continuity Conditions at Potential Steps waves · matter
D-011	Tunnelling Through a Rectangular Barrier waves · matter · energy · chance	verified
D-010	The Harmonic Oscillator via Ladder Operators energy · symmetry · matter	verified
D-146	Oscillator Eigenfunctions and Hermite Polynomials energy · waves · matter
D-012	Free Gaussian Wave Packet and Its Spreading waves · matter · chance	verified
D-147	Measurement, Collapse, and Spectral Expansion chance · symmetry
D-148	The Time-Evolution Operator and Energy Basis Dynamics energy · symmetry · waves

PU-203 · Thermal & Statistical Physics I 17

D-149	The Ideal Gas Law from Kinetic Theory matter · energy · force
D-015	Carnot's Theorem and Maximum Engine Efficiency energy	verified
D-150	The Clausius Inequality and Entropy as a State Function energy · chance
D-151	Thermodynamic Potentials via Legendre Transforms energy
D-152	Equilibrium as Free-Energy Minimization energy · matter
D-016	The Maxwell Relations energy · symmetry	verified
D-153	Stability, Convexity, and Positive Response Functions energy · matter
D-154	The Clausius-Clapeyron Relation energy · matter
D-155	Boltzmann Entropy and Statistical Temperature chance · energy
D-013	The Boltzmann Distribution chance · energy	verified
D-156	The Partition Function and F = -kT ln Z chance · energy
D-157	Energy Fluctuations and Heat Capacity chance · energy
D-158	Equivalence of Ensembles in the Thermodynamic Limit chance
D-014	The Maxwell-Boltzmann Speed Distribution chance · matter	verified
D-020	Equipartition and Its Failure energy · chance	verified
D-017	Sackur-Tetrode Entropy and the Gibbs Paradox chance · matter · symmetry	verified
D-159	The Grand Canonical Ensemble and Chemical Potential chance · matter

PU-204 · Electromagnetism II 18

D-160	Faraday's Law and the Flux Rule fields · force · energy
D-161	The Displacement Current from Charge Conservation fields · symmetry
D-162	Assembly of Maxwell's Equations fields · symmetry
D-163	Potentials and Gauge Freedom fields · symmetry
D-164	Electromagnetic Wave Equation in Vacuum waves · light · fields
D-165	Structure of Monochromatic Plane Waves waves · light · fields
D-166	Poynting's Theorem and Field Energy energy · fields · waves
D-167	Maxwell Stress Tensor and Field Momentum force · energy · fields
D-168	Retarded Potentials and Jefimenko's Equations fields · waves
D-169	Fields of a Moving Point Charge fields · force · waves
D-170	Larmor Formula for Radiated Power energy · waves · light
D-171	Electric Dipole Radiation waves · light · energy
D-172	Reflection, Refraction and Fresnel Equations waves · light · fields
D-173	Waves in Conductors and Skin Depth waves · matter · fields
D-174	Dispersion from the Lorentz Oscillator Model waves · matter · light
D-175	The Electromagnetic Field Tensor fields · symmetry
D-176	Relativistic Transformation of E and B fields · symmetry · force
D-177	Field Lagrangian and Gauge Invariance symmetry · fields · energy

PU-205 · Mathematical Methods II — Complex Analysis & Asymptotics 18

D-178	Cauchy-Riemann Equations & Harmonic Conjugates fields · symmetry
D-179	Cauchy-Goursat Theorem fields
D-180	Cauchy Integral Formula & Derivative Formula fields · symmetry
D-181	Taylor Series of Analytic Functions
D-182	Laurent Series & Classification of Singularities
D-183	The Residue Theorem fields
D-184	Real Integrals by Residues & Jordan's Lemma waves
D-185	Argument Principle & Rouché's Theorem
D-186	Branch Points, Cuts & Riemann Surfaces symmetry
D-187	Analytic Continuation & the Identity Theorem symmetry
D-188	Gamma Function: Continuation & Reflection Formula chance · symmetry
D-189	Conformal Mapping & Plane Potential Theory fields
D-190	Asymptotic Series & Optimal Truncation
D-191	Watson's Lemma chance
D-192	Laplace's Method for Exponential Integrals chance · energy
D-193	Method of Steepest Descent chance · energy
D-019	Stirling's Formula via Saddle Point chance	verified
D-194	Method of Stationary Phase waves · light

PU-206 · Optics 18

D-195	Optical Wave and Helmholtz Equations from Maxwell light · waves · fields
D-196	The Eikonal Equation as the Short-Wavelength Limit light · waves
D-197	Fermat's Principle from the Eikonal Equation light · symmetry
D-198	Laws of Reflection and Refraction from Fermat light · symmetry
D-199	Paraxial Ray-Transfer (ABCD) Matrices light
D-200	Lensmaker's Formula and the Imaging Equation light
D-201	Fresnel Equations from Electromagnetic Boundary Conditions light · fields · energy
D-202	Brewster's Angle, Total Internal Reflection, and Evanescent Waves light · fields
D-203	Polarization States and the Jones Calculus light · symmetry · fields
D-204	Dispersion and Absorption from the Lorentz Oscillator light · matter · fields
D-205	Phase Velocity, Group Velocity, and Pulse Spreading waves · light
D-206	The Helmholtz-Kirchhoff Diffraction Integral light · waves
D-207	Fraunhofer Diffraction as a Fourier Transform light · waves
D-208	Diffraction Grating: Grating Equation and Resolving Power light · waves
D-209	Airy Pattern and the Rayleigh Resolution Limit light · waves
D-210	Gaussian Beams from the Paraxial Wave Equation light · waves
D-211	The van Cittert-Zernike Coherence Theorem light · waves · chance
D-212	Abbe Theory of Imaging and Spatial Filtering light · waves

PU-301 · Quantum Mechanics II 18

D-213	Spectral Theorem for Hermitian Observables chance · symmetry
D-214	Generalized Uncertainty Relation chance · waves
D-215	Angular Momentum Spectrum from Commutators symmetry · matter
D-216	Spherical Harmonics as Angular Momentum Eigenstates symmetry · waves · matter
D-217	Separation of the Central-Potential Schrodinger Equation energy · symmetry · waves
D-218	Hydrogen Atom Bound-State Spectrum energy · matter · fields
D-219	Spin-1/2 and the Pauli Matrices symmetry · matter
D-220	Addition of Angular Momenta symmetry · matter
D-221	Non-Degenerate Perturbation Theory energy · chance
D-222	Degenerate Perturbation Theory energy · symmetry
D-223	Fine Structure of Hydrogen energy · matter · symmetry · fields
D-224	Rayleigh-Ritz Variational Principle energy · chance
D-225	WKB Approximation and Bohr-Sommerfeld Quantization waves · energy
D-226	Time-Dependent Perturbation Theory energy · chance · waves
D-227	Fermi's Golden Rule energy · chance · light
D-228	Electric Dipole Transitions and Selection Rules light · symmetry · matter
D-229	Identical Particles and Exchange Symmetry matter · symmetry · chance
D-230	Born Approximation and Partial Waves waves · matter · chance · symmetry

PU-302 · Statistical Mechanics 18

D-231	Boltzmann Entropy from Microstate Counting chance · energy
D-232	Temperature, Pressure and Chemical Potential from Entropy Maximization energy · chance
D-233	Boltzmann Distribution from a Heat Reservoir energy · chance
D-156	The Partition Function and F = -kT ln Z chance · energy
D-234	Gibbs Entropy and the Maximum-Entropy Derivation of the Ensembles chance · energy
D-235	Grand-Canonical Ensemble and the Grand Potential chance · matter · energy
D-157	Energy Fluctuations and Heat Capacity chance · energy
D-236	Equivalence of Ensembles in the Thermodynamic Limit chance · energy
D-237	The Equipartition Theorem energy · chance
D-238	The Gibbs Paradox and Indistinguishability matter · chance · symmetry
D-239	Ideal Gas Law and Sackur-Tetrode Entropy matter · energy · chance
D-240	Bose-Einstein and Fermi-Dirac Occupation Numbers matter · chance · symmetry
D-241	Planck's Law from the Photon Gas light · chance · energy · matter
D-242	Debye Model of Phonon Heat Capacity matter · waves · energy · chance
D-243	Degenerate Fermi Gas and the Sommerfeld Expansion matter · chance · energy
D-244	Bose-Einstein Condensation matter · chance · symmetry · energy
D-245	Mean-Field Ising Model and Spontaneous Magnetization fields · chance · symmetry · matter
D-246	Landau Theory and Critical Exponents symmetry · fields · chance · energy

PU-303 · Condensed Matter Physics 18

D-247	Reciprocal Lattice from the Bravais Lattice matter · symmetry · waves
D-248	Laue and Bragg Diffraction Conditions waves · matter · symmetry
D-249	Bloch's Theorem from Translational Symmetry symmetry · waves · matter
D-250	Band Gaps in the Nearly-Free-Electron Model waves · energy · symmetry
D-251	Tight-Binding Band Dispersion waves · energy · matter
D-252	Effective Mass and Semiclassical Electron Dynamics energy · waves · fields
D-253	Density of States and Van Hove Singularities energy · waves · matter
D-254	Sommerfeld Free-Electron Heat Capacity energy · chance · matter
D-255	Phonon Dispersion of the Diatomic Chain waves · matter · energy
D-256	Quantization of Lattice Vibrations waves · matter · energy
D-257	Debye Model and the T-cubed Heat Capacity energy · waves · chance
D-258	Intrinsic Carrier Concentration in Semiconductors chance · energy · matter
D-259	Electrical Conductivity from the Boltzmann Equation fields · energy · chance
D-260	Landau Levels and the Integer Quantum Hall Effect fields · matter · symmetry
D-261	Cooper Pair Instability energy · matter · chance
D-262	BCS Gap Equation and the Superconducting Gap energy · matter · symmetry · chance
D-263	Weiss Mean-Field Theory of Ferromagnetism matter · fields · chance · symmetry
D-264	Spin-Wave Dispersion and Magnons waves · matter · symmetry

PU-304 · Nuclear & Particle Physics 18

D-265	Semi-Empirical Mass Formula from the Liquid-Drop Model energy · matter · force
D-266	Coulomb Energy of a Uniformly Charged Nucleus energy · fields · force
D-267	Asymmetry Term from the Fermi-Gas Model energy · matter · chance
D-268	The Valley of Beta Stability energy · matter
D-269	Gamow Factor and the Geiger-Nuttall Law energy · chance · matter
D-270	Fermi's Golden Rule chance · energy · waves
D-271	Fermi Theory of Beta Decay and the Kurie Plot chance · energy · force · matter
D-272	Radioactive Decay and Bateman Equations chance · matter
D-273	Rutherford Scattering Cross-Section force · fields · chance
D-274	Born Approximation and the Form Factor waves · fields · chance
D-275	Mandelstam Invariants and Relativistic Two-Body Kinematics energy · symmetry
D-276	Lorentz-Invariant Phase Space and the Decay/Cross-Section Master Formulae energy · chance · symmetry
D-277	Klein-Gordon Equation and the Yukawa Potential waves · fields · force
D-278	Dirac Equation, Antiparticles and the g=2 Prediction matter · symmetry · waves
D-279	Noether's Theorem for Conserved Currents symmetry · energy · fields
D-280	Local U(1) Gauge Invariance Fixes the QED Coupling symmetry · fields · force
D-281	Isospin, Hypercharge and the Gell-Mann-Nishijima Relation symmetry · matter
D-282	Spontaneous Symmetry Breaking and the Higgs Mechanism symmetry · fields · force · matter

PU-305 · Classical Electrodynamics 18

D-283	Laplacian of 1/r as a Delta Function fields
D-284	Gauss's Law from Coulomb's Law fields · force
D-285	Electrostatic Potential and Irrotational E fields · energy
D-286	Energy Stored in the Electric Field energy · fields
D-047	Multipole Expansion of the Potential fields · symmetry
D-287	Bound Charge and the Displacement Field fields · matter
D-052	Ampère's Circuital Law from Biot–Savart fields · symmetry
D-288	Vector Potential and Bound Currents fields · matter
D-289	Faraday's Law and the Induced Field fields · energy
D-290	Displacement Current and Maxwell's Equations fields · symmetry
D-291	Poynting's Theorem energy · fields · waves
D-167	Maxwell Stress Tensor and Field Momentum force · energy · fields
D-164	Electromagnetic Wave Equation in Vacuum waves · light · fields
D-292	Fresnel Equations at an Interface waves · light · matter
D-293	Retarded Potentials in Lorenz Gauge fields · waves
D-170	Larmor Formula for Radiated Power energy · waves · light
D-294	Covariant Formulation of Electrodynamics symmetry · fields · light
D-295	Transformation of E and B under Boosts symmetry · fields

PU-306 · Atomic & Molecular Physics 18

D-296	Separation of the Central-Potential Schrodinger Equation energy · matter · waves · symmetry
D-297	Bound-State Spectrum of the Hydrogen Atom energy · matter · waves · symmetry
D-298	Relativistic Kinetic-Energy Correction energy · matter
D-299	Spin-Orbit Coupling from the Rest Frame energy · fields · matter · symmetry
D-300	Fine-Structure Energy Formula energy · matter · symmetry · light
D-301	Hyperfine Splitting and the 21 cm Line energy · fields · matter · light
D-302	Anomalous Zeeman Effect and the Lande g-Factor energy · fields · matter · symmetry
D-303	Linear Stark Effect in Hydrogen energy · fields · matter · symmetry
D-304	Exchange Symmetry and the Ortho/Para Splitting matter · symmetry · energy
D-305	Variational Ground-State Energy of Helium energy · matter
D-306	The Hartree-Fock Self-Consistent-Field Equations energy · matter · symmetry
D-307	LS Coupling, Term Symbols, and Hund's Rules matter · symmetry · energy
D-308	Electric-Dipole Selection Rules light · symmetry · waves
D-309	Einstein Coefficients and Spontaneous Emission light · energy · chance · waves
D-310	The Born-Oppenheimer Approximation energy · matter · waves
D-311	The Hydrogen Molecular Ion and the Chemical Bond energy · matter · symmetry
D-312	Molecular Rotational and Vibrational Spectra energy · matter · waves · light
D-313	The Franck-Condon Principle light · matter · waves · energy

PU-307 · Fluid Dynamics 18

D-314	Reynolds Transport Theorem matter · symmetry
D-315	The Continuity Equation matter · symmetry
D-316	Existence of the Cauchy Stress Tensor force · matter
D-317	Cauchy's Momentum Equation force · matter · symmetry
D-318	Navier-Stokes from the Newtonian Constitutive Law force · matter · fields
D-319	Euler's Equations as the Inviscid Limit force · energy · fields
D-320	Bernoulli's Theorem, Steady and Unsteady energy · force
D-321	The Vorticity Transport Equation fields · force · symmetry
D-322	Kelvin's Circulation Theorem symmetry · fields
D-323	Potential Flow and Laplace's Equation fields
D-324	D'Alembert's Paradox force · fields · symmetry
D-325	Stokes Drag on a Sphere force · matter
D-326	The Reynolds Number from Nondimensionalisation symmetry · force
D-327	Energy Balance and Viscous Dissipation energy · matter
D-328	The Acoustic Wave Equation and Speed of Sound waves · energy · matter
D-329	Prandtl's Boundary-Layer Equations force · fields
D-330	Dispersion of Surface Gravity Waves waves · energy · fields
D-331	Kolmogorov's Four-Fifths Law chance · energy · symmetry

PU-308 · Astrophysics & Cosmology 18

D-332	Equation of Stellar Hydrostatic Equilibrium force · energy
D-333	Virial Theorem for Bound Systems energy · force
D-334	The Lane-Emden Equation for Polytropes force · energy · matter
D-335	The Chandrasekhar Mass Limit matter · chance · force · energy
D-336	Tolman-Oppenheimer-Volkoff Equation fields · force · matter · energy
D-337	The Saha Ionization Equation chance · matter · energy
D-338	The FRW Metric from Homogeneity and Isotropy symmetry · fields
D-339	The Friedmann Equations from Einstein's Equations fields · energy · symmetry · force
D-340	Cosmological Redshift from the Scale Factor light · waves · symmetry
D-341	Comoving, Luminosity, and Angular-Diameter Distances light · symmetry
D-342	Particle Horizon, Horizon and Flatness Problems symmetry · light · fields
D-343	Slow-Roll Inflation from a Scalar Field fields · energy · symmetry · chance
D-344	CMB Blackbody Spectrum and T ∝ 1/a light · chance · symmetry
D-345	Recombination and Photon Decoupling light · matter · chance
D-346	Primordial Helium from Big Bang Nucleosynthesis matter · chance · energy
D-347	The Jeans Instability Criterion force · waves · matter
D-348	Linear Growth of Density Perturbations matter · force · chance
D-349	Flat Rotation Curves and Dark Matter Halos force · matter

PU-401 · Advanced Quantum Theory 18

D-350	Interaction Picture and the Dyson Series energy · chance
D-227	Fermi's Golden Rule energy · chance · light
D-351	Semiclassical Radiation and Dipole Selection Rules light · matter · symmetry
D-352	Einstein A and B Coefficients light · chance · energy
D-353	Addition of Angular Momenta symmetry · matter
D-354	The Wigner-Eckart Theorem symmetry · matter
D-355	The Rayleigh-Ritz Variational Bound energy
D-356	WKB Approximation and Connection Formulas waves · energy
D-357	Gamow Tunneling and Alpha Decay waves · energy · chance · matter
D-358	The Adiabatic Theorem energy · chance
D-359	Berry's Geometric Phase symmetry · fields · waves
D-360	The Lippmann-Schwinger Equation waves · matter
D-361	The Born Approximation waves · matter · chance
D-362	Partial-Wave Analysis and Phase Shifts waves · matter · symmetry
D-363	The Optical Theorem waves · chance · energy
D-229	Identical Particles and Exchange Symmetry matter · symmetry · chance
D-364	The Density Matrix and von Neumann Equation chance · matter
D-365	The Feynman Path Integral waves · chance · energy

PU-402 · Lagrangian Field Theory 18

D-366	Euler-Lagrange Equations for Fields fields · energy
D-367	Noether's First Theorem symmetry · energy · fields
D-368	Canonical Stress-Energy Tensor energy · symmetry · fields
D-369	Belinfante-Rosenfeld Improvement energy · symmetry · fields
D-370	Klein-Gordon Field from Its Lagrangian fields · waves · matter
D-371	Representations of the Lorentz Group symmetry · matter · fields
D-372	Dirac Equation from the Spinor Lagrangian matter · fields · symmetry
D-373	Maxwell's Equations from −¼F² light · fields · force · symmetry
D-374	Local U(1) Gauge Invariance and Minimal Coupling symmetry · force · fields
D-375	Proca Field and Its Degrees of Freedom fields · force · matter
D-376	Hamiltonian Formulation for Fields energy · fields
D-377	Canonical Quantization of a Field fields · matter
D-378	Mode Expansion and Fock Space waves · matter · fields
D-379	The Feynman Propagator fields · waves · matter
D-380	Conserved Charge as Symmetry Generator symmetry · fields
D-381	The Spin-Statistics Theorem symmetry · matter · fields
D-382	Goldstone's Theorem symmetry · fields · matter
D-383	The Abelian Higgs Mechanism symmetry · force · fields · matter

PU-403 · General Relativity 18

D-384	Equivalence Principle Forces a Curved Metric force · symmetry · fields
D-385	Geodesic Equation from Extremal Proper Time force · energy · symmetry
D-386	Covariant Derivative and the Metric Connection symmetry · fields
D-387	Riemann Tensor from the Covariant Commutator symmetry · fields
D-388	Parallel Transport and Geodesic Deviation force · fields
D-389	Contracted Bianchi Identity and the Einstein Tensor symmetry · energy
D-390	Stress-Energy Tensor as the Conserved Source energy · symmetry · matter
D-391	Field Equations from the Einstein-Hilbert Action energy · fields · symmetry
D-392	Newtonian Limit Fixes the Coupling Constant force · energy · fields
D-393	Schwarzschild Solution from Spherical Vacuum fields · symmetry · force
D-394	Perihelion Precession from Schwarzschild Orbits force · energy
D-395	Light Deflection and Gravitational Redshift light · energy · force
D-396	Event Horizon and Maximal Extension fields · symmetry · light
D-397	Linearized Gravity and the Wave Equation waves · fields · light
D-398	Quadrupole Formula for Radiated Power waves · energy
D-399	Friedmann Equations from the FLRW Metric energy · fields · symmetry
D-400	Cosmological Redshift and Hubble's Law light · waves · energy
D-401	Raychaudhuri Equation and Geodesic Focusing energy · fields · force

PU-404 · Quantum Information & Computation 18

D-402	The No-Cloning Theorem chance · symmetry · matter
D-403	Reduced States and the Partial Trace chance · matter
D-404	Schmidt Decomposition of Bipartite States symmetry · chance · matter
D-405	Quantum Channels: Kraus and Stinespring chance · symmetry
D-406	CHSH Inequality and the Tsirelson Bound chance · light · matter
D-407	Quantum Teleportation chance · matter · symmetry
D-408	Superdense Coding chance · matter
D-409	Universality of CNOT with Single-Qubit Gates symmetry
D-410	The Solovay-Kitaev Theorem symmetry
D-411	Deutsch-Jozsa Oracle Separation chance · symmetry · waves
D-412	Grover Search and Its Optimality chance · waves · symmetry
D-413	The Quantum Fourier Transform Circuit waves · symmetry
D-414	Quantum Phase Estimation waves · symmetry · chance
D-415	Shor's Algorithm: Order Finding and Factoring symmetry · chance · waves
D-416	Von Neumann Entropy and Subadditivity chance · energy
D-417	The Holevo Bound chance · light
D-418	Landauer's Erasure Principle energy · chance
D-419	Stabilizer Codes and Error Discretization chance · symmetry · matter