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Article overview
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How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? | | M. Brics
; J. Kaupuzs
; R. Mahnke
; | | Date: |
21 Mar 2013 | | Abstract: | 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
ightarrowinfty, 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. | | Source: | arXiv, 1303.5211 | | Services: | Forum | Review | PDF | Favorites | |
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