Quasi-exactly solvable Fokker-Planck equations

Choon-Lin Ho; Ryu Sasaki

doi:10.1016/j.aop.2007.12.001

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arXiv · 0705.0863

Quasi-exactly solvable Fokker-Planck equations

Choon-Lin Ho·Ryu Sasaki

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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 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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cond-mat.stat-mech cond-mat.other hep-th math-ph math.MP nlin.SI quant-ph

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Choon-Lin Ho, Ryu Sasaki. 2007-05-07. Quasi-exactly solvable Fokker-Planck equations. https://doi.org/10.1016/j.aop.2007.12.001

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