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

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

2007-08-16

arxiv.org/abs/0708.2236v1

Physics

Quantum Physics

Scientific paper

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-Schr\"{o}dinger perturbation theory, no matrix elements need to be calculated. The method is applied to the Schr\"{o}dinger equation and the non-polynomial potential $V(r)=r^2+\frac{b r^2}{(1+cr^2)}$ in three dimensions is discussed as an illustrative example.

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