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arxiv: 0705.0863 · v2 · pith:SE2IDM6Mnew · submitted 2007-05-07 · ❄️ cond-mat.stat-mech · cond-mat.other· hep-th· math-ph· math.MP· nlin.SI· quant-ph

Quasi-exactly solvable Fokker-Planck equations

classification ❄️ cond-mat.stat-mech cond-mat.otherhep-thmath-phmath.MPnlin.SIquant-ph
keywords fokker-planckequationequationslistedquasi-exactlysolvabilitysolvableturbiner
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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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