POWER-SERIES EXPANSION FOR THE TIME EVOLUTION OPERATOR WITH A HARMONIC-OSCILLATOR REFERENCE SYSTEM

A simple framework for accurate solution of a general class of one-dimensional Fokker-Planck and/ or Schrodinger equations is presented. The main idea is representing the propagator in the form P(x,t/x(0)) = P-0(x,t/x(0))exp[W(x,t/x(0))] and expanding the exponent W in a power series in a given function of t, where Po is the exact solution of a reference harmonic-oscillator problem. The expansion coefficients are analytically evaluated from recursive relations. This approach is shown to be a dramatic improvement over the standard Taylor series expansion for the propagator in that just a few terms of the present expansion are sufficient to attain a very accurate description in the whole time domain.