Transition moment integrals and the hypervirial theorem. I

Abstract

Hypervirial theorems are used to derive a differential equation for the transition-moment generating function (A mod exp(itx) mod B) associated with eigenstates A and B in a one dimensional wave- mechanical system. Explicit solution of the equation is possible for the harmonic oscillator, and leads to a simple expression for the overlap integral between two similar oscillators on different centres.