scopal affairsSchrödinger 2D
A wave packet runs through a grid of obstacles and fills the field with interference. Calculated in two dimensions, rendered as video.
A Gaussian wave packet moves through a two-dimensional landscape of obstacles. The video shows the probability density |ψ|²: the brighter a point, the greater the density.
The packet meets a triangular grid of pegs (a Galton board). As it scatters, the waves overlap. Interference patterns form and, in the end, fill the whole square. At the edge an absorbing layer damps the wave so that it does not re-enter on the opposite side.
The calculation solves the time-dependent Schrödinger equation with the split-operator method: each time step takes two Fourier transforms, the kinetic part in momentum space, the potential part in position space. The video has 500 frames at 30 frames per second (1024 × 1024 pixels). It was made in a Pluto notebook in Julia.