Energetic spectrum of a particle in three-dimensional infinite potential square well in point of view of number theory and Bayesian statistics

Abstract

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.