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arXiv · 2310.17210

Summation formulas generated by Hilbert space eigenproblem

Petar Mali·Sonja Gombar·Slobodan Radoševi\' c·Milica Rutonjski·Milan Panti\' c·Milica Pavkov-Hrvojevi\' c
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Abstract

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.

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Petar Mali, Sonja Gombar, Slobodan Radoševi\' c, Milica Rutonjski, Milan Panti\' c, Milica Pavkov-Hrvojevi\' c. 2023-10-26. Summation formulas generated by Hilbert space eigenproblem. https://arxiv.org/abs/2310.17210

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