Summation formulas generated by Hilbert space eigenproblem
Petar M. Mali, Sonja Gombar, Slobodan Radošević, Milica S. Rutonjski, Milan R. Pantić, Milica V. Pavkov-Hrvojević · Journal of Mathematical Physics · 2024
We demonstrate that certain classes of Schlömilch-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.