https://doi.org/10.1140/epjp/s13360-022-03634-2
Regular Article
Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
1
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
a
alonso.contreras@conacyt.mx
c
cesar.muro@cinvestav.mx
Received:
19
September
2022
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.
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