Some new considerations about the $ν$-function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914944128122880 |
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| author | Popov, Dušan |
| author_facet | Popov, Dušan |
| contents | The present paper starts from a previously deduced result, in which the $ν$-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 $ν$-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 $ν$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some new considerations about the $ν$-function Popov, Dušan Quantum Physics 81R30 Coherent states, 33C90 Applications of hypergeometric functions, 33E20 Other functions defined by series and integrals The present paper starts from a previously deduced result, in which the $ν$-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 $ν$-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 $ν$-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. |
| title | Some new considerations about the $ν$-function |
| topic | Quantum Physics 81R30 Coherent states, 33C90 Applications of hypergeometric functions, 33E20 Other functions defined by series and integrals |
| url | https://arxiv.org/abs/2409.05476 |