Related papers: Using quantum mechanics for calculation of different infinite sums

Using quantum mechanics for calculation of different infinite sums

URL: http://arxiv.org/abs/2109.03080v1
Date: Tue, 7 Sep 2021 13:36:01 GMT
Title: Using quantum mechanics for calculation of different infinite sums
Authors: Petar Mali, Milica Rutonjski, Slobodan Rado\v{s}evi\'c, Milan Panti\'c, Milica Pavkov-Hrvojevi\'c
Abstract summary: We show that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem. This method can be applied to a wide class of exactly quantum mechanical problems which may lead to different infinite sums.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the problem of a particle in a box. Twofold calculation of the mean value of energy for the polynomial wave function inside the well yields even argument $p$ ($p>2$) of Riemann zeta and related functions. This method can be applied to a wide class of exactly solvable quantum mechanical problems which may lead to different infinite sums. Besides, the analysis performed here provides deeper understanding of superposition principle and presents useful exercise for physics students.

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