New version of the Rayleigh-Schrodinger perturbation theory:: Examples

It has been shown in our preceding papers that the linear dependence of the perturbation wave functions on the perturbation energies makes possible to calculate the exact perturbation energies from the values of the perturbation wave functions corresponding to arbitrarily chosen trial perturbation energies. The resulting version of the perturbation theory is very simple and can be used at large orders. In this paper, this method is applied to a few problems and its numerical properties are discussed. (C) 2004 Wiley Periodicals, Inc.