Schrödinger's Equation and Discrete Random Walks in a Potential Field

Abstract 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 extend this result to show that the original random walk system may be modified to include a smooth temperature field which locally alters the walker's expected mean free path. This modification effects the correlations in such a way that Schrodinger's free particle equation aquires a potential term.