Open Access

Using supermodels in quantum optics

Advances in Difference Equations20062006:072768

DOI: 10.1155/ADE/2006/72768

Received: 27 January 2006

Accepted: 12 April 2006

Published: 5 September 2006

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.

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Authors’ Affiliations

(1)
Fakultät für Mathematik, Technische Universität München

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Copyright

© N. Garbers and A. Ruffing 2006

This article is published under license to BioMed Central Ltd. 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.