This article shows that the asymptotic quantum mechanical exchange energies and wave functions in a bistable potential can be obtained by computing the complex-valued first-passage time across the potential barrier from a transient state endowed with Smoluchowski boundary conditions, whose probability density is concentrated on one side of the barrier. This interpretation is validated by one of the authors' previous work on diffusion in a random field, showing that this model yields a diffusion equation equivalent to quantum mechanical equations. (C) 2001 American Institute of Physics.