Swipe to Collapse

Overview This app displays a real-time simulation of the two-dimensional Schrödinger equation. A quantum wave function lives on the grid. Its colour is the phase and its brightness is how likely the particle is to be there (|ψ|²). You play by observing it.

Observe Drag across the field to outline a region, then let go to measure it. The wave collapses by the Born rule — the particle is either found inside your region (it snaps bright there) or not (that area goes dark). Pick a stage and try it freely before starting a game.

Game Tap Start for a 30-second round. Green particles roam the field and score continuously — the brighter the wave |ψ| where a particle sits, the faster it scores. Observe (drag) to collapse the wave and pile it onto the green particles. Red particles (stage 2+) drain your score the same way, so keep the wave dark around them. Best 3 scores per stage are saved. Tap × to quit.

Z/pZ Lab — position & momentum together An experimental mode on the finite set Z/pZ, where position and momentum are both finite and the Fourier transform links them. Two strips show \psi(x) and \hat{\psi}(k) at once — drag either one to observe in that basis. The carpet below charts the wave over time; watch the fractal revivals. Switch p, potential, kinetic term, initial state and more.