On the one-dimensional Coulomb Hamiltonian

Abstract

A rigorous definition is given of the one-dimensional Coulomb Hamiltonian, discuss its spectral properties, and investigate various approximations for it. For one of these approximations, which is frequently used in the literature, it is proven in particular that it converges to the semi-bounded Coulomb Hamiltonian in the strong graph limit, although its ground-state tends to minus infinity in this limit.