Quantum and classical stochastic dynamics: Exactly solvable models by supersymmetric methods

Abstract

A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of drift-potentials on the real line as well as on the half line is constructed for which the associated Fokker-Planck equation can be solved exactly. Explicit drift potentials, which describe mono-, bi-, meta-or unstable systems, are constructed and their decay rates and modes are given in closed form.