Abstract
A method for solving the Smoluchowski equation for arbitrary potential energy surfaces in any number of dimensions is presented. The method is based on the postulate that the time evolution of the probability density at sufficiently short times and for sufficiently small space increments is separable into a diffusion component and a deterministic component. The method is verified by observing that a known analytic solution to the Smoluchowski equation for the case of a particle diffusing isotropically in a parabolic one-dimensional potential can be duplicated to any desired degree of accuracy by choosing small enough space and time increments. The method is also applied to the case of a single particle diffusing isotropically in a periodic potential, and to the case of two-dimensional conformational diffusion about the glycosidic torsion angles of maltose oligomers within the torsion angle conformational potential.
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