An Interpretation of the Squared Amplitude of a Solution of the Schrodinger Wave Equation

It is found that that from a mathematical standpoint the probability density given by a solution of the Schrodinger wave equation is determined by an underlying random variable which has a Chi-Square distribution with one degree of freedom, and that the resulting mean probability density agrees with its deterministic value in quantum mechanics. As a result quantum probability and interference patterns in particular, would obey the normal laws of probability.