Supersymmetry and Bistable Soft Potentials

The diffusion of a Brownian particle is investigated for a class of potentials (soft bistable) which resist conventional techniques. A new method of solution based on supersymmetric quantum mechanics is shown to provide, with minimal effort, an accurate determination of the small eigenvalue of the relevant Fokker-Planck equation. The reciprocal of the small eigenvalue compares very closely with a refined definition of mean first-passage time.