Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states

• URL: http://arxiv.org/abs/2304.05461v2
• Date: Thu, 24 Aug 2023 17:33:34 GMT
• Title: Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states
• Authors: Juan D Garc\'ia-Mu\~noz and David J Fern\'andez C and F Vergara-M\'endez
• Abstract summary: The algebras are generated by the multiphoton and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The Barut-Girardello coherent states, which are annihilations of the operator, are obtained and their uncertainty relations are explored.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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