Variational supersymmetric approach to evaluate Fokker–Planck probability

G.R.P. Borges, Elso Drigo Filho and R.M. Ricotta

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 18, 3892-3899

Abstract: In this work we introduce a method to determine the time dependent probability density for the one-dimensional Fokker–Planck equation. The treatment is based in an analysis of the Schrödinger equation through the variational method associated to the formalism of supersymmetric quantum mechanics (SQM). The approach uses an ansatz for the superpotential which allows us to obtain the trial functions of the variational method. The hierarchy of effective Hamiltonians permits us to determine the variational eigenfunctions and energies of the excited states to the evaluation of the probability. The symmetric bistable potential is used to illustrate the approach whose results are compared with results obtained by the state-dependent diagonalization method and by direct numerical calculation.

Keywords: Fokker–Planck equation; Bistable potential; Variational method; Supersymmetry (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:18:p:3892-3899

DOI: 10.1016/j.physa.2010.05.027

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