On the Coulomb Sturmian matrix elements of relativistic Coulomb Green's operators

Abstract

The Hamiltonian of the radial Coulomb Klein-Gordon and second order Dirac equations are shown to possess an infinite symmetric tridiagonal matrix structure on the relativistic Coulomb Sturmian basis. This allows us to give an analytic representation for the corresponding Coulomb Green's operators in terms of continued fractions. The poles of the Green's matrix reproduce the exact relativistic hydrogen spectrum.