Application of variational method and supersymmetric technique to the fokker-planck equation

The time dependent probability density for the one-dimensional Fokker-Planck equation is determined by the variational method within the context of the Supersymmetric Quantum Mechanics. Using an ansatz function for the superpotential, one can obtain the trial wavefunctions of the variational method and then the construction of the hierarchy of the effective Hamiltonians allows us to obtain the variational eigenfunctions and energies of the excited states to the evaluation of the probability. The symmetric bistable potentials, whose energy eigenvalues are calculated for some potential parameters, are studied. The numerical results obtained in this study are in very good agreement with the eigenvalues obtained by numerical integration in previous studies. The error percent is also presented in all calculations.