Improved wave functions for large-<i>N</i>expansions

Abstract

Existing large-N expansions of radial wave functions ${\ensuremath{\varphi}}_{n}$,l(r) are only accurate near the minimum of the effective potential. Within the framework of the shifted 1/N expansion, we use known analytic results to motivate a simple modification so that the improved wave functions are accurate over a wide range of r and any choice of quantum numbers n and l. It is shown that these wave functions yield simple and accurate analytic expressions for certain quantities of interest in quarkonium physics.