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Using supermodels in quantum optics

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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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Author information

Correspondence to Nicole Garbers.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Quantum Mechanic
  • Ordinary Differential Equation
  • Functional Analysis