SCHRODINGERS EQUATION AND CLASSICAL BROWNIAN-MOTION

In the context of quantum mechanics, Schrodinger's equation has many p ossible interpretations, none of which appear to be entirely satisfact ory. One reason for this is that there is no known microscopic model w hich yields both Schrodinger's equation and an accompanying 'sensible' interpretation. In contrast to this the diffusion equation is well kn own as a phenomenological equation obtainable from the microscopic mod el of Brownian motion. In this case the microscopic model provides an unambiguous interpretation of the partial differential equation. In th is article we review work which shows that Schrodinger's equation by i tself is also easily obtained from a lattice random walk Version of th e Brownian motion model. In this system, Schrodinger's equation arises by projection and the interpretation of wave functions is as direct a nd unambiguous as the interpretation of density in the diffusion case. However the direct interpretation is compatible with quantum mechanic s only in a statistical sense in the context of ensembles of particles . This shows that measurement theory is the aspect of quantum theory w hich harbours the problems of interpretation, and we suggest the study of this and related systems to clearly illuminate the boundary betwee n dynamics and measurement.