How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?

An analogy of the Fokker-Planck equation (FPE) with the Schr dinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrodinger potential with discrete eigenvalue spectrum. Here we will show how this approach can be applied also for mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=±L/2 and take the limit L→∞, considering examples with constant Schr dinger potential and with P schl-Teller potential. An oversimplified approach has been earlier proposed by M.T. Araujo and E. Drigo Filho. A detailed investigation of the two examples shows that the correct solution, obtained in this paper, is consistent with the expected Fokker-Planck dynamics.