Bounds on second-order energies in stationary perturbation theory

Abstract

Upper and lower bounds are derived for the second-order energy of any state of any atomic system. These bounds require only a knowledge of the unperturbed wave function of the state under consideration and some knowledge of the unperturbed energy spectrum. These bounds have been applied to the calculation of the ground-state energies of two-electron atoms and to the polarizabilities of the ground state of one- and two-electron atoms.