Deformed Fokker-Planck Equations

Abstract

Based on the well-known relation between Fokker-Planck equations and Schroedinger equations of quantum mechanics (QM), we propose new deformed Fokker-Planck (FP) equations associated with the Schroedinger equations of "discrete" QM. The latter is a natural discretization of QM and its Schroedinger equations are difference instead of differential equations. Exactly solvable FP equations are obtained corresponding to exactly solvable "discrete" QM, whose eigenfunctions include various deformations of the classical orthogonal polynomials.