Image method solutions for free-particle wave packets
arXiv:quant-ph/0512108 · doi:10.1088/0143-0807/27/2/011
Abstract
Using analogs of familiar image methods in electrostatics and optics, we show how to construct closed form wave packet solutions of the two-dimensional free-particle Schrodinger equation in geometries restricted by two infinite wall barriers separated by an angle Theta = pi/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a pi/3 = 60 degree wedge. We review the time-development of zero-momentum wave packets placed near a single infinite wall barrier in an Appendix.
14 pages, 4 figures, to appear in Eur. J. Phys