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