  A revised iterative method based on Green function defined by quadratures
along a single trajectory is proposed to solve the low-lying quantum wave
function for Schroedinger equation. Specially a new expression of the perturbed
energy is obtained, which is much simpler than the traditional one. The method
is applied to solve the unharmonic oscillator potential. The revised iteration
procedure gives exactly the same result as those based on the single trajectory
quadrature method. A comparison of the revised iteration method to the old one
is made using the example of Stark effect. The obtained results are consistent
to each other after making power expansion.
