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Spinnor

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### Derivation of the Schrödinger Equation from Newtonian Mechanics

### Edward Nelson Phys. Rev. 150, 1079 – Published 28 October 1966

Abstract,

"We examine the hypothesis that every particle of mass m is subject to a Brownian motion with diffusion coefficient ℏ2m and no friction. The influence of an external field is expressed by means of Newton's law F=ma, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schrödinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent."

Can someone think of a simple argument why we should expect interference in Nelson's work above given the initial assumptions? For example consider a simple case of a particle in one dimensional box. Where does quantization of energy and momentum come from in what seem like simple assumptions of his work.

Thanks.