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

✍ Scribed by G.N. Ord

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
185 KB
Volume
250
Category
Article
ISSN
0003-4916

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✦ Synopsis

It has been recently noted that the free particle Schro dinger 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 Schro dinger's free particle equation aquires a potential term.

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