Derivation of the Schrödinger Equation from Newtonian Mechanics
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 OrnsteinUhlenbeck 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.
 Publication:

Physical Review
 Pub Date:
 October 1966
 DOI:
 10.1103/PhysRev.150.1079
 Bibcode:
 1966PhRv..150.1079N