Quantum Wavepacket — Schrödinger in Any Potential

One solver for every one-dimensional scattering and bound-state problem in the textbook. A Crank-Nicolson integrator — unitary, O(N) via the Thomas algorithm, and norm-preserving to machine precision — evolves a minimum-uncertainty Gaussian wavepacket through any potential: six are built in (free propagation, rectangular barrier, finite square well, harmonic oscillator, double barrier, potential step) alongside a custom expression field for arbitrary V(x). Sliders set the potential strength (in units of the packet’s kinetic energy), the barrier or well width, the wavenumber k₀, and the animation speed. A 3D Argand diagram renders ψ as a complex helix whose pitch is the de Broglie wavelength, while a synchronized panel tracks |ψ|² against the potential with live norm, transmission/reflection coefficients, and centre-of-mass readouts.