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.

8 pages, no figures. Sect. IV.C rewritten, and other places slightly modified accordingly. New references added

References in corpus (2)

• Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators
• Quasi-exact solvability of Dirac equation with Lorentz scalar potential

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