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It is assumed that every particle of mass, m, undergoes random submicroscopic fluctuations of position and momemtum. The Schrö dinger equation is the derived from classical mechanics and the assumed Markov process in 6-dimensional phase space. The Markov process, which is hypothesized for the motion of a particle, is not equivalent to Brownian motion.
Millard Baublitz (Mon,) studied this question.
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