No particles. Only wavefunctions. Observe and they collapse.
P(x) = |ψ(x, t)|²
Toni Giorgino, LLM-coded.
The 2D Schrödinger equation, solved live in your browser. ħ = m = 1.
Each chapter teaches one idea. Every level has a one-line physics point, and the full explanation is one click away.
| Setup | Drag the packet to move it, the arrow head to set its momentum, the ring to set its width σ. Inventory items: add, drag, resize with their handles; Del removes. |
|---|---|
| Space | Play / pause (starts the run from the setup) |
| Enter | Observe: sample |ψ|², collapse, win or lose. At the end of the clock the world observes for you. |
| Click the field | Kick (when the level has charges): a momentum impulse toward the cursor |
| Arrows / WASD | Field tilt (when available): a uniform force while held |
| 1–9 | Toggle gates; fire detectors (hold to pulse a "hold" detector) |
| R | Back to setup, same dice |
| [ ] | Previous / next level |
| V C G M | Cycle view, probability current, ghost preview, sound |
| ? Esc | This sheet; close panels |
Hue = phase, brightness = |ψ|. Orange tint = potential barrier, blue = well, rings = harmonic equipotentials, purple = absorber. The hatched frame is the absorbing edge: probability that reaches it is lost.
Polarization view: hue = polarization axis (red horizontal, green 45°, cyan vertical, violet −45°), white = circular. Optics show their axis on a dial: violet polarizer, amber rotator, teal plate, pink Stern–Gerlach magnet (axis goes up), red bomb station.
Timeline: the faint curve is the ghost preview of PT(t) for the current setup with no real-time actions, the bright one is this run, dashed lines are the star thresholds.
Each horizontal band of the field is a note of a pentatonic scale, loud as √P in that band; on headphones a concentrated packet is heard from its x position (HRTF), a spread-out ψ from all around; faster packets sound brighter. The bells are Born-rule samples of |ψ|², a high halo grows with PT, a low beating drone with PM. Observation fades it all to silence.