  An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger
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 Schr\"odinger potential with a discrete eigenvalue spectrum.
Here, we will show how this approach can be also applied to a mixed eigenvalue
spectrum with bounded and free states. We solve the FPE with boundaries located
at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples
with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential.
An oversimplified approach was proposed earlier 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.
