Math
Physics

This java applet is a quantum mechanics simulation that shows the behavior of a particle in a two-dimensional crystal (or periodic potential).

At the top of the applet you will see a graph of the particle's wave function. By default, the potential is an array of rectangular square wells; the gray lines indicate the positions of the wells.

Below the particle's position you will see its band structure, displayed as a dispersion curve; this is a graph of energy versus the crystal momentum k, with the energy bands shown as gray in the background. The particle's energy is shown as a red horizontal line.

Below the dispersion curve is a graph of the reciprocal lattice, or "k-space". The colored dots correspond to the colored lines in the band structure graph.

To view a state, click on either the dispersion curve or the k-space graph.