Phase dynamics in the quantum stadium billiard
Channel: Nils Berglund
Date: 06/06/2021

A solution of Schrödinger's equation in a stadium-shaped domain. This simulation shows the same quantum evolution as the video https://youtu.be/32ry0ZtSOvI with a different color code: the luminosity represents the probability of finding the particle (modulus of the wave function squared), while the hue represents the phase (argument of the wave function).  The initial state is a Gaussian wave packet located on the horizontal symmetry axis, with a vertical upward momentum. The probability density concentrates near classical trajectories moving up and down between the straight parts of the boundary, a feature known as "scars" in quantum chaos.

Music: "Haunted Forest" by TrackTribe@TrackTribe

The simulation solves the Schrödinger equation by discretization. 
The C code can be found on https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html 

Many thanks to my colleague Marco Mancini for helping me to accelerate my code!

You may be interested in some science outreach articles: https://images.math.cnrs.fr/_Berglund-Nils-1343_.html