Quantum Mirror Focusing by Iterating the Schrodinger Equation

This animation shows the two dimensional (2D) propagation of s gaussian envelope wave packet as governed by the Schrodinger equation. In this case I have chosen the initial packet to be rectangular with gaussian boundaries. The Mirror is a shaped potential concave spherical shape with gaussian reflecting edges. The energies of the wave packet and the mirror are color coded. The color of the initial wave packet center is associated with the kinetic energy (kx*kx/2) of the packet. The color of the bulk of the mirror is the potential energy. These energies are adjustable using the kx and the Mirror Potential Sliders. Note that the mirror potential must be greater than the packet potential energy if reflection and focusing is desired, The color bar (Peak Energies) shows the learner the relative values of these energies. The position expected for the packet to focus is at mirror radius divided by 2 from the apex of the mirror which is shown by a white vertical bar. Note that both the height andwidth of the packet are greatly reduced at this focus. I believe that this quantum mirror could be realized in practice by forming an array of charged particles with boundaries on the concave surface of the mirror. 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 parameters 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that when you see significant reflections from the upper and lower bounds of the gridded region that the plot data is no longer valid.

The total desktop computer time for completion of the mirror focus is usually about 1 minute.