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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.

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