Learn

Short lessons that explain the physics step by step, in plain words. Topics are listed in the order to learn them. Lessons marked draft have not been reviewed yet.

Classical mechanics

How everyday objects move, from a thrown ball to the planets, and the elegant reformulations behind it.

2 of 46 lessons written

Foundations

The tools every later lesson uses.

  • Units, dimensions and estimation planned
  • Vectors and coordinate systems planned
  • Calculus for physics: rates and accumulation planned
  • Differential equations: laws as rules for change planned

Describing motion

Kinematics: how things move, before asking why.

Newton's laws

Why things move: forces and acceleration.

  • Newton's three laws planned
  • Gravity, normal force, tension, friction and springs planned
  • Free-body diagrams and problem solving planned
  • Drag and terminal velocity planned
  • Why we simulate: from Euler to RK4 planned

Energy and momentum

Quantities that stay constant, and what that buys you.

  • Work, energy and conservation of energy planned
  • Potential energy curves and equilibrium planned
  • Momentum, impulse and collisions planned
  • Centre of mass and systems of particles planned
  • Variable mass and rocket motion planned

Oscillations

Back-and-forth motion, the pattern behind clocks, bridges and atoms.

  • Simple harmonic motion planned
  • Damped oscillations planned
  • Driven oscillations and resonance planned
  • The pendulum and nonlinear oscillations planned
  • Phase space: seeing the whole motion at once planned

Gravitation and central forces

Planets, orbits and the effective potential.

  • Universal gravitation planned
  • Torque and angular momentum planned
  • Central forces and the effective potential planned
  • Kepler's laws and orbit shapes planned
  • Precession and perturbed orbits planned

Rotation and rigid bodies

Spinning things.

  • Moment of inertia and rotational dynamics planned
  • Rolling motion planned
  • Gyroscopes and precession planned
  • Non-inertial frames: centrifugal and Coriolis forces planned

Lagrangian and Hamiltonian mechanics

The same physics from a more powerful point of view; the bridge to quantum mechanics.

  • Calculus of variations and the principle of least action planned
  • Lagrangian mechanics and Euler–Lagrange equations planned
  • Constraints and generalized coordinates planned
  • Symmetry and Noether's theorem planned
  • Hamiltonian mechanics and Hamilton's equations planned
  • Poisson brackets and canonical transformations planned

Coupled systems, waves and chaos

Many parts moving together, and when prediction breaks down.

  • Coupled oscillators and normal modes planned
  • Waves on a string and the wave equation planned
  • Fourier analysis: building any shape from waves planned
  • Dispersion, phase and group velocity planned
  • Chaos, the double pendulum and Lyapunov exponents planned

Beyond Newton (overview)

Where classical mechanics stretches and where it breaks.

  • Special relativity in one lesson planned
  • Continuum mechanics and fluids: a first look planned
  • The limits of classical physics planned

Quantum mechanics

How the very small behaves: waves of probability, discrete energies, and spin.

0 of 42 lessons written

Why quantum mechanics

The experiments that broke classical physics.

  • Why we need quantum mechanics planned
  • Blackbody radiation and the photoelectric effect planned
  • Atomic spectra and the Bohr model planned
  • Wave–particle duality and the double slit planned

The wavefunction

The central object of quantum mechanics.

  • The wavefunction and the Born rule planned
  • Expectation values and uncertainty planned
  • The Schrödinger equation planned
  • Stationary states and the time-independent equation planned
  • Probability current and conservation of probability planned

Quantum mechanics in one dimension

Solvable systems that teach the key ideas.

  • Free particles and wave packets planned
  • The infinite square well planned
  • The quantum harmonic oscillator planned
  • The finite square well and bound states planned
  • The delta-function potential planned
  • Scattering and quantum tunnelling planned
  • Double wells, superposition and revivals planned

The mathematical framework

States as vectors, observables as operators.

  • Linear algebra for quantum mechanics planned
  • Hilbert space and Dirac notation planned
  • Operators, observables and Hermiticity planned
  • Commutators and the uncertainty principle planned
  • Measurement and collapse planned
  • Time evolution and Ehrenfest's theorem planned
  • The classical limit and the correspondence principle planned

Three dimensions and atoms

From a line to the real world.

  • The Schrödinger equation in three dimensions planned
  • Angular momentum and spherical harmonics planned
  • The hydrogen atom planned
  • Identical particles and the Pauli exclusion principle planned
  • Atoms and the periodic table planned

Spin and qubits

The simplest quantum systems of all.

  • Spin-½ and the Pauli matrices planned
  • The qubit and the Bloch sphere planned
  • Quantum gates as rotations planned
  • Two-level systems and Rabi oscillations planned
  • Density matrices and decoherence planned

Approximation methods

What to do when an exact answer does not exist.

  • Time-independent perturbation theory planned
  • The variational method planned
  • The WKB approximation planned
  • Time-dependent perturbation theory planned

Beyond a single particle

Entanglement and the modern picture.

  • Entanglement planned
  • Bell's theorem and the EPR paradox planned
  • The path integral view planned
  • A first look at quantum computing planned
  • Interpretations of quantum mechanics planned