Quantum mechanics
States, operators, and the variational principle.
Learning sequence
- State, measurement, and operators — Connect amplitudes to outcomes and derive the uncertainty bound.
- Schrödinger dynamics and the box — Derive quantized energies from boundaries and distinguish superpositions.
- Harmonic oscillator and zero-point motion — Use ladder operators to derive levels and the Gaussian ground state.
- Variational principle and finite bases — Prove the ground-state bound and minimize a Gaussian trial family.
Read in sequence. Each lesson states its assumptions, derivation steps, and domain of validity.
