iℏ ∂ψ/∂t = [−ℏ²/2m · ∂²/∂x² + V(x)] ψ
Real-time 3D visualization of quantum wave packet propagation, barrier tunneling, and wavefunction collapse — rendered entirely in your browser with WebGL and Three.js.
A complete quantum physics lab with real-time controls for every parameter. Visualize the invisible mechanics underlying the universe.
Numerically solves the time-dependent Schrödinger equation using a split-operator method, giving accurate wavefunction evolution and tunneling probabilities every frame.
Watch a Gaussian wave packet evolve in real time as it travels toward a potential barrier. The simulation solves iℏ∂ψ/∂t = Ĥψ numerically and updates the 3D visualization every frame.
Adjust momentum k₀ to control how much energy the packet has relative to the barrier height. Below-threshold packets tunnel; above-threshold packets transmit classically.
Display stationary eigenstates of the Hamiltonian — probability densities that don't change shape over time. Only the global phase oscillates as e−iEt/ℏ.
Useful for understanding bound states, energy quantization, and the relationship between energy and tunneling probability without wave packet spreading.
Visualize quantum probability on a 3D sphere. Multiple wave packets launch from the surface; tunneling and reflection dynamics render as a 3D particle cloud around the sphere.
A live radial probability plot shows the angular distribution, analogous to hydrogen atom orbital density maps viewed from a new perspective.
| Parameter | Description |
|---|---|
| k₀ — Momentum | Wave vector; sets packet energy vs. barrier height |
| σ — Width | Gaussian std-dev; narrower = broader momentum spread |
| V₀ — Barrier Height | Above particle E → tunneling; below → classical pass |
| d — Barrier Width | Wider = exponentially less tunneling probability |
| Speed | Simulation time multiplier; slow for fine detail |
| Particles | Cloud density; more = accurate |ψ|² but slower |
| Key | Action |
|---|---|
| SPACE | Pause / Resume simulation |
| R | Reset wave packet to initial state |
| M | Trigger measurement — collapse ψ |
| V | Toggle Cloud ↔ Surface view |
| 1 / 2 | Switch Time-Dep / Time-Ind mode |
| S | Toggle Sphere 3D mode |
No setup. No install. Open the simulation and start exploring quantum mechanics immediately — full 3D physics, in your browser.