Large-order shifted 1/N expansions through the asymptotic iteration method

Abstract

The perturbation technique within the framework of the asymptotic iteration method is used to obtain large-order shifted 1/N expansions, where N is the number of spatial dimensions. This method is contrary to the usual Rayleigh–Schrödinger perturbation theory, no matrix elements need to be calculated. The method is applied to the Schrödinger equation, and the non-polynomial oscillator potential is discussed as an illustrative example.