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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.

Between each graph is a horizontal line which may be dragged up and down to adjust the size of each graph.

The Setup Popup allows you to select a predefined potential. The choices are:

The Mouse Popup determines what happens when the mouse is clicked. The choices are:

The Ground State button selects the ground state wave function.

The Stopped checkbox stops the evolution of the wave function.

The Simulation Speed slider changes the speed of the wave function evolution.

The Particle Mass slider changes the mass of the particle.

The # of Wells Shown slider changes the number of wells displayed. There are an infinite number of wells extending off to the left and right, but the applet shows a finite number of them.

The Energy Scale slider lets you display more of the energy spectrum by adjusting the scale used to graph energy.

The View Menu has the following items:

The Zones Menu allows you to specify which zone scheme to use when displaying the dispersion curve.

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