Article ID Journal Published Year Pages File Type
974093 Physica A: Statistical Mechanics and its Applications 2010 8 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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