An affine Weyl group characterization of polynomial Heisenberg algebras

Morales-Salgado, V S

doi:10.1016/j.aop.2022.169037

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2023

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“…In addition, if for the SUSY partners of the harmonic oscillator Hamiltonian the multiphoton annihilation and creation operators are employed, then additional polynomial Heisenberg algebras can be generated. Let us note that the harmonic oscillator Hamiltonian and its SUSY partners are almost the only systems for which the corresponding algebras have been explored [22,23,[26][27][28][29]. Thus, it is natural to ask ourselves if it is possible to implement a similar approach for other one dimensional potentials (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric quantum mechanics, multiphoton algebras and coherent states

García-Muñoz,

Fernández C,

Vergara-Méndez

2023

Phys. Scr.

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The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The algebras obtained turn out to be polynomial deformations of the corresponding single-photon algebra previously studied. The Barut-Girardello coherent states, which are eigenstates of the annihilation operator, are obtained and their uncertainty relations are explored by means of the associated quadratures.

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