Quantum Mechanics Based on Probability Wave Functions Induced by the Minimum Mean Deviation from Statistical Equilibrium. I

摘要

The maximum entropy probability distributions are generally used as probabilistic models for describing statistical equilibrium subject to given mean values of some random variables. The paper deals with the construction of probability wave functions by minimizing the mean deviation from statistical equilibrium subject to generalized correlations, induced by random fluctuations, whose values are determined looking for stationary points of the mean energy of the system. The results are applied to the study of several quantum systems (the free particle in a box, two independent particles in a box, the harmonic oscillator, and the hydrogen atom, without having to solve the corresponding Schrodinger equation.