Abstract
Self-consistent-field (SCF) methods are developed for solution of multidimensional diffusion problems. Time-dependent self-consistent-field (TDSCF) equations are derived for the Smoluchowski diffusion equation, and are applied to a two-dimensional barrier crossing problem. This is compared to both time-dependent and time-independent SCF approximations derived for the Schrödinger equation in imaginary time, which is obtained by transformation of the diffusion equation. Results for the model problem show that the TDSCF approximation for the original diffusion equation is accurate, efficient, and readily implementable in higher dimensions. Applications to diffusion problems in condensed media are noted.
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