Solutions of the Fokker-Planck equation for a Morse isospectral potential

Abstract

This work explores the relation between the Fokker-Planck equation and the Schrodinger equation in order to study solutions for the first one. The starting point is the study of the Schrodinger equation for a Morse potential. The next step is to determine the isospectral potential by using the formalism of supersymmetric quantum mechanics. Quantum isospectral potentials have the same energy spectrum of the original Morse potential, but the wavefunctions are different. Therefore, the transition probability that results from the Fokker-Planck equation for the Morse isospectral potential is different from that obtained for the original potential. This approach generates an entire class of new results.