English

Summation formulas generated by Hilbert space eigenproblem

Quantum Physics 2024-03-05 v4

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.

Keywords

Cite

@article{arxiv.2310.17210,
  title  = {Summation formulas generated by Hilbert space eigenproblem},
  author = {Petar Mali and Sonja Gombar and Slobodan Radoševi\' c and Milica Rutonjski and Milan Panti\' c and Milica Pavkov-Hrvojevi\' c},
  journal= {arXiv preprint arXiv:2310.17210},
  year   = {2024}
}

Comments

12 pages, 1 figure

R2 v1 2026-06-28T13:02:29.032Z