Shifted1Nexpansions for energy eigenvalues of the Schrödinger equation

Abstract

The $\frac{1}{N}$ expansion is a useful way of solving the Schrödinger equation to very high orders. We present a modified, physically motivated approach, called the shifted $\frac{1}{N}$ expansion, which dramatically improves the analytic simplicity and convergence of the perturbation series for the energy eigenvalues.