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Schrödinger Wave Packet: Quantum Field Dynamics (2D)

A real 1D time-dependent Schrödinger equation solver: a Gaussian wave packet evolves against a free, barrier, well or harmonic potential while norm, position and energy expectation values update live.

Quantum Physics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryQuantum Physics

RenderingCanvas 2D

DifficultyAdvanced

Target FPS60

ControlsPick a potential shape (free / step barrier / square well / harmonic), then drag the barrier-height, initial-momentum, packet-width and time-speed sliders to reshape the wavefunction's evolution live; Reset packet reseeds the Gaussian and Pause/Resume freezes the integration.

schrodinger-equationwave-packetquantum-tunnelingwavefunctionfinite-differenceprobability-density

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The 3D original renders quantum field dynamics as a decorative, shader-driven particle cloud with no underlying wave equation. This 2D companion replaces that decoration with a genuine physics engine: it integrates the real 1D time-dependent Schrödinger equation for a Gaussian wave packet using Visscher's staggered leapfrog finite-difference scheme, against a selectable free, barrier, well or harmonic potential, and reads out the conserved norm, ⟨x⟩ and ⟨E⟩ = ⟨T⟩+⟨V⟩ live from the grid.

⚙ Under the hood

A real 1D Schrödinger-equation solver (Visscher leapfrog finite differences) evolves a Gaussian wave packet against a free, barrier, well or harmonic potential, reading out conserved norm, mean position and energy live — including transmitted/reflected probability across a barrier.

schrodinger-equationwave-packetquantum-tunnelingwavefunctionfinite-differenceprobability-density

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install