Advances in Difference Equations
Volume 2006 (2006), Article ID 72768, 14 pages
doi:10.1155/ADE/2006/72768
Using supermodels in quantum optics
Fakultät für Mathematik, Technische Universität München, Boltzmannstraße 3, Garching 85747, Germany
Received 27 January 2006; Revised 11 April 2006; Accepted 12 April 2006
Copyright © 2006 Nicole Garbers and Andreas Ruffing. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Starting from supersymmetric quantum mechanics and related supermodels within Schrödinger theory, we review the meaning of self-similar superpotentials which exhibit the spectrum of a geometric series. We construct special types of discretizations of the Schrödinger equation on time scales with particular symmetries. This discretization leads to the same type of point spectrum for the referred Schrödinger difference operator than in the self-similar superpotential
case, hence exploiting an isospectrality situation. A discussion is opened on the question of how the considered energy sequence and its generalizations serve the understanding of coherent states in quantum optics.