Algebraic method for solving the Dirac equation with a Coulomb potential

The Dirac-equation energy spectrum with a Coulomb potential is solved by means of a purely algebraic method. First a part of the spectrum is found in a self-consistent way and then the complete spectrum is found with the (algebraic) results of a previous paper. Also the quadratic Dirac-equation spectrum is discussed to analyse a way of extracting the physical part out of it, i.e. that part which corresponds to the linear Dirac equation with a Coulomb potential.