The continuum Schroedinger-Coulomb and Dirac-Coulomb Sturmian functions

Spherical continuum Sturmian functions for the Schroedinger-Coulomb and Dirac-Coulomb problems are constructed by solving appropriate Sturm-Liouville systems. It is proved that in the non-relativistic case a spectrum of potential strengths is continuous and covers the whole real axis. In the relativistic case two Sturmian sets may be derived. For the relativistic Sturm-Liouville problems their eigenvalue spectra consist of the real axes with zero excluded plus circumferences in the complex plane centred at zero. It is shown that, as a consequence of a relationship existing between the two families of the continuum Dirac-Coulomb Sturmians, each family obeys two orthogonality and two closure relations. (author)