A NEW SUM RULE AND SOME SIMPLE $APPLICATIONS^{\dagger}$

Abstract

A new sum-rule is derived for certain sums of the form \[ \Sigma^{\prime}_{i}\frac{<0|A_{op}.|i>\;<i|B_{op}.|o>}{E_{i}-E_{o}} \] The result is exact and involves no approximations such as energy averages, etc. The rule is applied to the study of two cases where the Hellmann-Feynman theorem yields incorrect forces if unperturbed wave functions are used to calculate the electron density: a) the neutral atom in a uniform electric field; b) the London-van der Waals interaction of two neutral atoms.