Related papers: Summation formulas generated by Hilbert space eigenproblem

Summation formulas generated by Hilbert space eigenproblem

URL: http://arxiv.org/abs/2310.17210v4
Date: Sun, 3 Mar 2024 11:35:20 GMT
Title: Summation formulas generated by Hilbert space eigenproblem
Authors: Petar Mali, Sonja Gombar, Slobodan Rado\v{s}evi\' c, Milica Rutonjski, Milan Panti\' c, Milica Pavkov-Hrvojevi\' c
Abstract summary: We show that certain classes of Schl" omilch-like infinite series and series can be calculated in closed form. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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