On the Eigenvalues of a Soluble Model of Coupled Molecular and Nuclear Hamiltonians

In this paper, a special type of soluble model corresponding to a coupled molecular and nuclear Hamiltonians H, the so-called generalized Friedrichs model, is considered. We aim to determine and provide the most important properties of the well-known Faddeev operator corresponding to H accommodating a number of discrete eigenvalues. Furthermore, we provide a formula for counting the multiplicity of discrete eigenvalues of H.