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

摘要

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 lowerhyphen;bound equation given by Gay and another given by Miller. A numerical application to the ground state of the twohyphen;electron atom is presented. Upper and lower bounds for the secondhyphen;order perturbation energy are also presented, and a general upper bound for inverse operators is obtained.