Quasi-exactly solvable Fokker–Planck equations

Abstract

We consider exact and quasi-exact solvability of the one-dimensional Fokker–Planck equation based on the connection between the Fokker–Planck equation and the Schrödinger equation. A unified consideration of these two types of solvability is given from the viewpoint of prepotential together with Bethe ansatz equations. Quasi-exactly solvable Fokker–Planck equations related to the sl(2)-based systems in Turbiner’s classification are listed. We also present one sl(2)-based example which is not listed in Turbiner’s scheme.