Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
CONACyT - Departamento de Física, Cinvestav, A.P. 14-740, 07000, Mexico City, Mexico
2 Canadian Quantum Research Center, 204-3002 32 Ave, V1T 2L7, Vernon, BC, Canada
3 Departamento de Física, Cinvestav, A.P. 14-740, 07000, Mexico City, Mexico
4 Unidad Querétaro, Cinvestav, 76230, Querétaro, Mexico
Accepted: 23 December 2022
Published online: 21 January 2023
In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent supersymmetric transformations. We construct ladder operators for these extensions as the product of the intertwining operators of both transformations. Then, we generate families of Barut–Girardello coherent states and analyze some of their properties as temporal stability, continuity on the label, and completeness relation. Moreover, we calculate mean-energy values, time-dependent probability densities, Wigner functions, and the Mandel Q-parameter to uncover a general non-classical behavior of these states.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.