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2013

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

Brics, M., Kaupuzs, J., Mahnke, R.

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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.

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