SCHRODINGERS EQUATION AND DISCRETE RANDOM-WALKS IN A POTENTIAL-FIELD

It has been recently noted that the free particle Schrodinger equation in 1+1 dimensions occurs naturally in the description of correlations in random walks. In this non-quantum context, wave function solutions describe features of ensembles of random walks on lattices and are as a consequence observable and easily interpreted. In this article we e xtend this result to show that the original random walk system may be modified to include a smooth temperature field which locally alters th e walker's expected mean free path. This modification effects the corr elations in such a way that Schrodinger's free particle equation aquir es a potential term. (C) 1996 Academic Press. Inc.