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

Abstract

An infinite system of linear equations is derived from the Schrödinger equation of an n-electron atomic system (n⩾3). 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 essential spectrum of the Hamiltonian of the n-electron atomic system). It is further shown that the method can be used to deal with the case of the diatomic molecule. The above result then permits one, both in the case of the n-electron atomic system and the diatomic molecule, to truncate the infinite system of equations in question with the assurance that as the size of the truncated system is increased, the energy eigenvalues computed from the truncated system will uniformly converge to those of the original infinite system.