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.
