arXiv:1303.5211 · Condensed Matter Physics

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

M. Brics, Kaupuzs, Mahnke

Published Mar 1, 2013• 31 citations

Abstract

An analogy of the Fokker-Planck 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 Schrödinger 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 = ±L/2 and take the limit L → ∞, considering the examples with constant Schrödinger potential and with Pöschl-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.

DOI: 10.5488/cmp.16.13002

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