Radically simplified proofs of the Weyl and Stenger inequalities concerning eigenvalues of self-adjoint operators

Abstract

Radically simplified proofs of the generalized Weyl inequality and the Stenger inequality for eigenvalues of self-adjoint operators is presented. The main application of these results lie in atomic and molecular physics. The generalized inequality has application in obtaining bounds on molecular energy levels in cases where the molecular hamiltonian can be written as a sum of several atomic ones and the Stenger inequality has application in putting bounds on energy levels of atomic and molecular resonances to which the Feshbach formalism applies.