Condensed Matter Physics, 2013, vol. 16, No. 1, 13002
DOI:10.5488/CMP.16.13002
arXiv:1303.5211
Title:
How to solve FokkerPlanck equation treating mixed eigenvalue spectrum?
Author(s):

M. Brics
( Institute of Physics, Rostock University, D18051 Rostock, Germany )
,


J. Kaupuzs
( Institute of Mathematics and Computer Science, University of Latvia, LV1459 Riga, Latvia )
,


R. Mahnke
( Institute of Physics, Rostock University, D18051 Rostock, Germany )

An analogy of the FokkerPlanck equation (FPE) with the Schrödinger 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 Schrödinger potential and with PöschlTeller 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 FokkerPlanck dynamics.
Key words:
FokkerPlanck equation, Schrödinger equation, PöschlTeller potential
PACS:
05.10.Gg
