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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.17210 |
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| _version_ | 1866917602199076864 |
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| author | Mali, Petar Gombar, Sonja c, Slobodan Radoševi\' Rutonjski, Milica c, Milan Panti\' c, Milica Pavkov-Hrvojevi\' |
| author_facet | Mali, Petar Gombar, Sonja c, Slobodan Radoševi\' Rutonjski, Milica c, Milan Panti\' c, Milica Pavkov-Hrvojevi\' |
| contents | We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an infinite potential well and using principles of quantum mechanics. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models. Obtaining series from normalization conditions in well-defined quantum problems secures their convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17210 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Summation formulas generated by Hilbert space eigenproblem Mali, Petar Gombar, Sonja c, Slobodan Radoševi\' Rutonjski, Milica c, Milan Panti\' c, Milica Pavkov-Hrvojevi\' Quantum Physics We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an infinite potential well and using principles of quantum mechanics. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models. Obtaining series from normalization conditions in well-defined quantum problems secures their convergence. |
| title | Summation formulas generated by Hilbert space eigenproblem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.17210 |