This article shows that the asymptotic quantum mechanical exchange energies
and wave functions in a bistable potential can be obtained by computing th
e complex-valued first-passage time across the potential barrier from a tra
nsient state endowed with Smoluchowski boundary conditions, whose probabili
ty 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 qu
antum mechanical equations. (C) 2001 American Institute of Physics.