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It is shown that the stationary states of the nonrelativistic Schr\"odinger's equation are just the stationary states of a classical-mechanical system which is subject to random submicroscopic fluctuations of position. The proof covers the case (1) of a single particle moving in a potential, and (2) of two particles interacting through a potential V (x₁-x₂). The results can be easily generalized to the case of n interacting particles.
David Kershaw (Mon,) studied this question.