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A General Solution of the Fokker-Planck Equation

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Abstract

The Fokker-Planck equation is useful to describe stochastic processes. Depending on the force acting in the system, the solution of this equation becomes complicated and approximate or numerical solutions are needed. The relation with the Schrödinger equation allows building a method to obtain solutions of the Fokker-Planck equation. However, this approach has been limited to the study of confined potentials, restricting its applicability. In this work, we suggest a general treatment for non-confining potentials through the use of series of functions based on the solution of the Schrödinger equation, with part of discrete spectrum and part of continuum spectrum. Two examples, the Rosen-Morse potential and a limited harmonic potential, are analyzed using the suggested approach.

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Authors and Affiliations

  1. Physics Department, Unesp, São José do Rio Preto, SP, Brazil

    M. T. Araujo & E. Drigo Filho

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  1. M. T. Araujo
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  2. E. Drigo Filho
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Correspondence to M. T. Araujo.

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Araujo, M.T., Drigo Filho, E. A General Solution of the Fokker-Planck Equation. J Stat Phys 146, 610–619 (2012). https://doi.org/10.1007/s10955-011-0411-8

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  • DOI: https://doi.org/10.1007/s10955-011-0411-8

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