Quasi-exactly solvable Fokker-Planck equations

Details Quasi-exactly solvable Fokker-Planck equations Quasi-exactly solvable Fokker-Planck equations

2007-05-07

arxiv.org/abs/0705.0863v2

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/j.aop.2007.12.001

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 Schr\"odinger 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.

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