The one-dimensional hydrogen atom in momentum representation

Abstract

A momentum representation treatment of the one-dimensional hydrogen atom with Coulomb interaction is presented. The authors obtain the energy levels and bound-state eigenfunctions for the problem and discuss the general properties of the solution. The energy spectrum is discrete and given by the Balmer formula. They show that, despite the symmetry of the potential, it is impossible to find eigenfunctions with definite parity for the system.