Energetic Spectrum of a Particle in Three-dimensional Infinite Potential Square Well in Point of View of Number Theory and Bayesian Statistics

Pavel Jahoda, Jan Kracik, David Ulcak

Energetic Spectrum of a Particle in Three-dimensional Infinite Potential Square Well in Point of View of Number Theory and Bayesian Statistics

Číslo: 2/2017
Periodikum: Advances in Electrical and Electronic Engineering
DOI: 10.15598/aeee.v15i2.2248

Klíčová slova: Asymptotic density; Bayesian inference; number theory; potential well, Asymptotická hustota; Bayesovský závěr; Teorie čísel; Potenciálně dobře.

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Anotace: Using results of number theory we develop an approximate statistical model of energy levels of particles in a three-dimensional infinite potential well depending on whether there is exactly one particle or more than one particles in the well. The model is used to perform a statistical inference about the number of particles in the well. The estimation procedure is developed within the Bayesian framework.