An application of the theta operator in generalized hypergeometric coherent states formalism

• URL: http://arxiv.org/abs/2404.13119v1
• Date: Fri, 19 Apr 2024 18:07:59 GMT
• Title: An application of the theta operator in generalized hypergeometric coherent states formalism
• Authors: Dušan Popov,
• Abstract summary: We examine one of the multiple applications of theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs) A series of new results were obtained and some already known ones were found / confirmed. To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this paper we examine one of the multiple applications of the theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs). These states are the most general coherent states, in the sense that from them, through particularization, all coherent states with physical meaning can be obtained. A series of new results were obtained and some already known ones were found / confirmed (the integral representations, as well as the Laplace transform of hypergeometric functions). To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum. The results obtained in this paper contribute to widening the area of applicability of the theta operator.

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