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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