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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. The brightness at a particular point indicates the probability of the particle being found at that point, and the color indicates phase. Only a part of the wave function is shown; the actual wave function extends to infinity.

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 energy at each point is shown by the background color; black is low energy, green is high energy, yellow is higher energy. Also, the white lines indicate contours of equal energy. The red line indicates all points with the same energy as the particle's current energy. The colored dots correspond to the vertical colored lines in the dispersion graph.

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

You may select a different potential from the Potential 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. Whenever you change the potential, it takes some time to calculate the band structure. The band structure will keep changing for maybe 10 seconds or so (depending on the speed of your computer) until it is fully calculated.

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

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 edges of the position graph, but the applet shows a finite number of them.

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

The Contour Count slider lets you adjust the density of the contour lines in k-space.

The Cell Height slider lets you adjust the height of the primitive cells. By default, the cell height is the same as the cell width. If you change this slider, you break that symmetry. Note the difference between this slider and the Well Height slider. Well Height allows you to change the amount of vertical space a well takes up within a primitive cell. Cell Height changes the size of a primitive cell.

The View Menu has the following items:

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