Improved Equation for Lower Bounds to Eigenvalues; Bounds for the Second-Order Perturbation Energy

Abstract

Using the bounding theorems given by Eqs. (1) and (2), an improved equation for lower bounds to eigenvalues is obtained [Eq. (8)]. This improved result is a generalization of an earlier lower‐bound equation given by Gay and another given by Miller. A numerical application to the ground state of the two‐electron atom is presented. Upper and lower bounds for the second‐order perturbation energy are also presented, and a general upper bound for inverse operators is obtained.