waves
A wave starts as a system nudged off balance and left to swing; it becomes a spectrum of allowed notes, then a spreading packet of probability, and finally something that leaks through walls it should not cross. "Waves" is the story of how oscillation, once counted in springs, learns to carry amplitude, energy, and probability at once.
Units touched PU-201 · PU-202 Adjacent threads energy · matter · chance Stations 5
The stations
Small oscillations as an eigenproblem
Any system near equilibrium rings at fixed normal-mode frequencies — the first hint that "wave" means eigenvalues, not just wiggles.
The continuity equation & probability current
The wavefunction is promoted to something conserved: amplitude now flows, and a current tracks where the wave carries probability.
Oscillator spectrum by ladder operators
The classical spring returns quantised — a discrete ladder of allowed energies, oscillation reborn as a spectrum of states.
Spreading of a free Gaussian wave packet
A localised wave will not stay put: dispersion spreads the packet, showing that a particle-like wave has a shape with its own dynamics.
Transmission through a rectangular barrier
The wave reaches a wall taller than its energy and comes out the other side — tunnelling, the endpoint where wave nature defies classical intuition.