Physics

Newton's first law and inertia

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Newton's second law and F=ma

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Newton's third law and conservation of momentum

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Free fall and projectile motion

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Circular motion and centripetal force

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Friction, normal force, and inclined planes

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Work, kinetic energy, and the work-energy theorem

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Conservation of energy

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Hooke's law and simple harmonic motion

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Torque, angular momentum, and rotational dynamics

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Moment of inertia and rigid-body rotation

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Central-force motion and Kepler's laws

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Two-body problem and reduced mass

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Lagrangian mechanics and the Euler-Lagrange equation

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Hamiltonian mechanics and phase space

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Noether's theorem and continuous symmetries

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Nonlinear dynamics and chaos

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Coulomb's law and the electric force

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Electric field of a point charge

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Electric field of a continuous charge distribution

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Gauss's law and field symmetries

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Electric potential and equipotential surfaces

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Capacitance and dielectric materials

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Current, resistance, and Ohm's law

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Kirchhoff's laws and DC circuits

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Magnetic field of a current-carrying wire

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Ampère's law and Biot-Savart

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Faraday's law of electromagnetic induction

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Lenz's law and induced EMF

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Self-inductance and mutual inductance

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RLC circuits and resonance

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Maxwell's equations in integral and differential form

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Electromagnetic waves in vacuum

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Poynting vector and EM energy flow

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Waveguides and resonant cavities

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Larmor formula and radiation from accelerating charges

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Multipole expansion of fields

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Ideal gas law and kinetic theory

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First law of thermodynamics

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Second law and entropy

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Heat engines and Carnot efficiency

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Refrigerators, heat pumps, and the Clausius statement

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Entropy from microstates: S = k ln Ω

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Maxwell-Boltzmann velocity distribution

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Partition function and canonical ensemble

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Helmholtz and Gibbs free energy

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Phase transitions and the Clausius-Clapeyron relation

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Critical phenomena and universality

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Black-body radiation and Planck's law

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Fermi-Dirac and Bose-Einstein statistics

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The wave equation and properties of waves

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Superposition and interference

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Standing waves, normal modes, and resonance

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Doppler effect for sound and light

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Refraction and Snell's law

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Geometric optics: lenses and mirrors

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Thin-film interference

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Young's double-slit experiment

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Single-slit diffraction and gratings

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Resolving power and the Rayleigh criterion

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Polarization of light and Malus's law

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Fourier optics and image formation

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Wave-particle duality

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The photoelectric effect

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de Broglie wavelength and matter waves

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Bohr model of the hydrogen atom

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Heisenberg uncertainty principle

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Time-independent Schrödinger equation

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Particle in an infinite square well

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Quantum harmonic oscillator and ladder operators

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Quantum tunneling and barrier penetration

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Hydrogen atom: separation of variables and quantum numbers

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Angular momentum operators and spherical harmonics

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Spin-1/2 and Pauli matrices

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Bra-ket notation and Hilbert space

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Time-dependent perturbation theory

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Time-independent perturbation theory

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WKB semiclassical approximation

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Path integral formulation

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Quantum entanglement and Bell's inequality

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Postulates of special relativity

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Time dilation and length contraction

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Lorentz transformations

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Relativistic energy and momentum

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The twin paradox

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Spacetime diagrams and invariant intervals

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Four-vectors and tensor index notation

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The equivalence principle

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Schwarzschild metric and black holes

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Geodesics and the Einstein field equations

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Gravitational waves

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FLRW metric and cosmological models

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The Standard Model overview

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Leptons, quarks, and the three generations

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QCD basics: quarks and the strong force

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Weak interactions and beta decay

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Higgs boson and mass generation

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Neutrino oscillations

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Feynman diagrams and scattering amplitudes

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Nuclear decay: alpha, beta, gamma

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Nuclear binding energy and the semi-empirical mass formula

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Renormalization and running couplings

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Crystal structure and Bravais lattices

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Reciprocal lattice and Brillouin zones

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Free electron model of metals

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Band theory and Bloch's theorem

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Semiconductors: p-n junctions and doping

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Phonons and lattice vibrations

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Superconductivity and BCS theory

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Integer and fractional quantum Hall effect

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Ferromagnetism and the Ising model

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Density functional theory

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Vector calculus: div, grad, curl

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Fourier series and Fourier transforms

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Complex analysis and contour integration

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PDEs: separation of variables

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Tensors and Einstein index notation

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Variational calculus and Euler-Lagrange

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Group theory for physicists

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Differential forms and Stokes' theorem

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