This java applet is a quantum mechanics simulation that shows the behavior of a particle in a one-dimensional crystal (or lattice, or periodic potential). Periodic potentials are used to model electron behavior in a crystal.

At the top of the applet you will see a graph of the potential, along with horizontal bands showing the energy levels. By default, the potential is an array of square wells (the Kronig-Penney model). Below that you will see the probability distribution of the particle's position. 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.

To view a state, click on one of the energy bands in either the potential graph or the dispersion curve.

You may select a different potential from the Setup menu at the top right. You can also adjust the parameters of the potential (like the width of the wells) using the sliders on the right.

Full Directions.

Java Version.

1-D Quantum Mechanics Applet.

Hydrogen Atom Applet.

2-D Crystal Applet.

Other applets.

Huge thanks to Bob Hanson and his team for help converting this applet to javascript.