Random walks and Schrödinger's equation in dimensions
- 7 February 1997
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 30 (3) , 819-830
- https://doi.org/10.1088/0305-4470/30/3/008
Abstract
Some recent results have shown that in addition to its role in quantum mechanics, the Schrödinger free particle equation in (1+1) dimensions describes second-order effects in ensembles of lattice random walks. This alternative classical context for Schrödinger's equation is independent of its role in quantum mechanics. In this paper we extend this result to include the case of Schrödinger's equation in (2+1) dimensions for a particle in a smooth bounded potential. The extension suggests that the new classical context of Schrödinger's equation is quite general.Keywords
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