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Please read this writeup for a description of the theory associated with this applet, and an accompanying set of exercises. Documentation of the applet itself is listed below.

This simulation demonstrates the scattering of an incoming wave on a one-dimensional crystal. The one-dimensional crystal is represented as a series of evenly-spaced atoms, each atom of which is modelled as a Dirac Delta Function. The simulation shows two windows, with a set of controls at the right.

The left window demonstrates graphically the parameters of the system. The x-axis represents position, and the y axis represents energy. In reality, y-axis represents momentum, but for a user not in the quantum-mechanics class, this can be thought of as energy. There are several objects in the left window, most of which can be adjusted. To adjust a parameter, one can drag the little red boxes attached to the adjustable objects.

The right window demonstrates the transmission of the wave through the crystal. There are no axes on the graphs yet, but they will be added soon. Pure reflection (hence no transmission) is represented by a point at the left of the graph, perfect transmission at the right side of the graph. The vertical axis of the graph representes momentum (ie, energy), and is calibrated to be equivalent to the vertical scale on the left window.

The right side of the applet contains a number of controls and outputs. That describes the current status of the program. One can now see the transmission of an incident travelling wave through the crystal, for a variety of different crystal situations. This is an interesting problem because there are cases where there is perfect transmission through the crystal, even if the incident energy is less than the strength of the crystal atoms. This program is mostly completed, there are a few more items that may be implemented. These aren't essential, but will help improve the user interface.

Jeffrey Wasserman
January 7, 2004