Related papers: Some new considerations about the $ν$-function

Some new considerations about the $ν$-function

URL: http://arxiv.org/abs/2409.05476v1
Date: Mon, 9 Sep 2024 10:08:17 GMT
Title: Some new considerations about the $ν$-function
Authors: Dušan Popov,
Abstract summary: We show that the $nu$-function plays the role of the normalization function of generalized hypergeometric coherent states for quantum systems with a continuous spectrum. To our knowledge, the results obtained by us do not appear in the literature.
Score: 0.0
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: The present paper starts from a previously deduced result, in which the $\nu$-function plays the role of the normalization function of generalized hypergeometric coherent states for quantum systems with a continuous spectrum. We have generalized this idea, obtaining a new function, the generalized $\nu$-function. By defining a discrete-continuous limit, we revealed a series of interesting properties that, in the last instance, allow the formulation and solution of new integrals involving the generalized $\nu$-functions which depend on both scalar arguments as well as those containing creation and annihilation operators, which generate the generalized hypergeometric coherent states. To our knowledge, the results obtained by us do not appear in the literature.

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