Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911778912337920 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in terms of $_3F_2$ hypergeometric functions. The O'Hara interesting interpretation of this Clebsch-Gordan coefficient by binomial random variables can also be related to hypergeometric functions ($_2F_1$), in the case where one of the parameters tends to infinity. This emphasizes the links between Clebsch-Gordan coefficients, hypergeometric functions and, what has been less exploited until now, the notion of probability within the framework of the quantum theory of angular momentum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution Pain, Jean-Christophe Mathematical Physics Atomic Physics A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in terms of $_3F_2$ hypergeometric functions. The O'Hara interesting interpretation of this Clebsch-Gordan coefficient by binomial random variables can also be related to hypergeometric functions ($_2F_1$), in the case where one of the parameters tends to infinity. This emphasizes the links between Clebsch-Gordan coefficients, hypergeometric functions and, what has been less exploited until now, the notion of probability within the framework of the quantum theory of angular momentum. |
| title | Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution |
| topic | Mathematical Physics Atomic Physics |
| url | https://arxiv.org/abs/2402.11298 |