Variational Perturbation Method Based on the Principle of Moments

Abstract

A simple practical variational perturbation method based on the approximate calculation of the moments of the resolvent operator is developed. The method has been applied to the $\mathrm{}\left(1S\right)\mathrm{}{}_{}{}^2{}_{}{}^{}S$ state of the helium atom. The trial wave functions have been expanded in terms of naturally spaced groups of Hylleraas functions up to 95 terms. The 95 term trial function gives an upper bound of -2.903724305 atomic units to the ground-state energy. Other numerical results have been compared with the 21st-order perturbation energies of Midtdal and other previous calculations. It is found that comparable results can be obtained by the present simple calculation.