Generalized hypervirial and recurrence relations for hydrogenic matrix elements

Abstract

A generalized expression for the second hypervirial of an arbitrary hydrogenic radial function is obtained. We illustrate the power of this result showing that a general recurrence relation among hydrogenic matrix elements becomes a simple consequence of it. We also exhibit that a particular case of such a recurrence relation can be rederived employing the hypervirial theorem and the well known mapping between the Morse and the Coulomb problems.