Two Mirror Quantum Resonator by Iterating the Schrodinger Equation

This animation shows the two dimensional (2D) propagation of a wave packet as governed by the Schrodinger equation. I have chosen to have the mirrors separated by 1/2 of the sum of their radii of curvature. In optics this is known as the concentric configuration. In this case I have chosen the initial packet to be rectangular with gaussian boundaries. I have chosen the start location of the packet to be at 1/2 of the radius of curvature from either mirror. Note that this is the normal focusing distance for the plane wave starting packet. The mirrors are concave potential cylinders with gaussian rolloff reflecting surfaces. The wave packet is color coded and the code is that shown on the color bar. The color of the bulk of the mirrors also corresponds to the potential energy. Note that the mirror potential must be greater than the packet kinetic energy, kx*kx/2, if reflection and focusing is desired. Many parameters are variable in this animation and they are pretty well defined by the titles of the sliders.

I have deliberately allowed the learner to adjust the variables beyond the ranges where valid propagation results are obtained. Important parameter for this are the pair (Gridding Half Height and kx) which, if made small enough, will easily run the diffracting wave packet beyond the gridded vertical half widths. Effectively, beyond the gridded width and height, the potential is infinite and results in strong reflections. Just be aware that when you see significant reflections from the bounds of the gridded region that the plot data is no longer valid.

The total desktop computer time for completion of a single round trip is usually about 30 seconds.