Quantum mechanics
Quantum mechanics
Eigenstates, wavepackets, and the geometry of solutions to the Schrödinger equation.
The modules are numbered in a suggested reading order, but each one stands on its own — select tags to narrow the list.
The Schrödinger equation
The evolution postulate, and why everything reduces to an eigenvalue problem.
- energy
- superposition
- dynamics
Measurement
The measurement postulate: possible outcomes, the Born rule, wavefunction collapse — and why the operator has to be Hermitian.
- measurement
- probability
- collapse
The ammonia maser
A two-level Hamiltonian with off-diagonal coupling: symmetric and antisymmetric states, the tunneling oscillation between them, and how it becomes a maser.
- energy
- measurement
- dynamics
The wavefunction
What is the wavefunction? How do we define it in position and momentum space, and how do we interpret it?
- wavefunction
- probability
Harmonic oscillator
Quantised energy levels and the zero-point energy.
- wavefunction
- energy
- superposition
- dynamics
Bound states of the finite well
Parity, the graphical construction, and how many states a well holds.
- wavefunction
- energy
- symmetry
Tunneling through a barrier
Transmission and reflection at a finite potential step.
- wavefunction
- dynamics
- probability
Particle in a 2D well
Separable states, and degeneracy as lattice points on an ellipse.
- wavefunction
- energy
- symmetry
- geometry
Atomic orbitals
3D electron density of hydrogen-like states, in spherical coordinates.
- wavefunction
- geometry
- atoms
Spin measurement
Successive measurements, collapse, and the Bloch sphere.
- measurement
- superposition
- probability
- geometry