The spectral properties of many-electron atomic Hamiltonians and the method of configuration interaction. II. Compactness proof associated with an infinite system of linear equations for two-electron atoms

Abstract

The Schrödinger equation for a two-electron atomic system is reduced to an infinite system of linear equations. The linear operator defined by this system of equations is then shown to be compact in a region of the complex energy plane which excludes the various bound state and multiparticle scattering cuts (i.e., the eseential spectrum of the Hamiltonian of the two-electron atomic system). This permits one to truncate the infinite system of equations with the assurance that the N energy eigenvalues obtained from the N×N truncated system will uniformly approximate the lowest N energy eigenvalues of the original infinite system.