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This work explores the relation between the Fokker-Planck equation and the Schrödinger equation in order to study solutions for the first one. The starting point is the study of the Schrödinger 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.

In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schrödinger type equation with a partially confining and symmetrical potential. To estimate the accuracy of the solution, a function error obtained from the original Fokker-Planck equation is suggested. Two examples, a truncated harmonic potential and non-harmonic polynomial, are analyzed using the proposed method. For the truncated harmonic potential, the system behavior as a function of temperature is also discussed.

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In literature the phenomenon of diffusion has been widely studied, however for nonextensive systems which are governed by a nonlinear stochastic dynamic, there are a few soluble models. The purpose of this study is to present the solution of the nonlinear Fokker-Planck equation for a model of potential with barrier considering a term of absorption. Systems of this nature can be observed in various chemical or biological processes and their solution enriches the studies of existing nonextensive systems.