NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.3, pp.336-343


On Solvable Potentials for One Dimensional Schrödinger and Fokker-Planck Equations.
George Krylov

Construction of exactly-solvable potentials for 1-dimensional Fokker-Planck equation is considered based on supersymmetric quantum mechanics approach. It is shown that a countable family of exactly-solvable potentials corresponds to every exactly-solvable Schrödinger equation and that both potentials and eigenstates of Fokker-Planck equation are expressed through Schrödinger's eigenfunctions. Among these families multi-well potentials with $log$-like discontinuity are possible. It is shown that such potentials are partially penetrable within the considered approach. New exactly-solvable Fokker-Planck equations possessing a mixed type spectrum of relaxation times have been constructed explicitly.
Key words: Fokker-Planck equation, supersymmetric quantum mechanics, exactly-solvable model, multi-well potential

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