Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations
arXiv:2109.03854 · doi:10.1016/j.cjph.2021.12.028
Abstract
A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schrödinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schrödinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained.
arXiv comment8 pages, no figures
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