Simulator for the Schrödinger equation

Physics

The simulator solves the time-evolution of a wavefunction according to the Schrödinger equation:

The initial state is a normalised Gaussian wavepacket in the position representation:

where $\Delta{x}$ is the variance of the position.

The dynamics of the wavepacket are simulated in an infinite potential well.

Solver

The Crank-Nicolson method is used to solve the Schrödinger equation numerically. More information about the mathematics behind the discretisation and solving of the equation are provided in the file crank_nicolson.pdf. The colors in the simulation represents the phase of the wavefunction at that given point.

Usage

The project was developed on and for Ubuntu, so it might not work on other systems. In a Bash terminal, running running the command:

./bin/run_animation

in the project root will produce a single .mp4 file of the time evolution.