Quantum mechanics · PDE numerics

Quantum Wavepacket — Schrödinger in Any Potential

Quantum Wavepacket — Schrödinger in Any Potential
fig. Quantum Wavepacket — Schrödinger in Any Potential

The notebook · live in your browser, code and all

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The notebook runs on its own once it loads, so give it about 10 seconds while Python starts up in your browser, and the simulations begin animating. Move the sliders and everything recomputes live. The code is shown alongside the output so you can read exactly how it works; the full editable source is linked below.

One solver for every one-dimensional quantum scattering problem in the textbook. A Gaussian wavepacket evolves under the time-dependent Schrodinger equation by a split-step method that stays unitary and conserves the norm, through any of six built-in potentials or one you type in yourself. The wavefunction is drawn as a 3D Argand helix: the real and imaginary parts live on perpendicular planes and the probability density sits on the floor, with the view tracking the packet as it moves and spreads. Below it, the live density reports the norm and the transmission and reflection coefficients.

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