Theory of involutional transformations applied to the Dirac theory of the electron. II. Remarks on the Dirac--Coulomb waves

By means of a single involutional transformation, the Dirac equation for a charged particle in a central Coulomb field is reduced to a second-order differential equation for the radial part which has the same form as the radial equation for the nonrelativistic Coulomb problem. The general Dirac--Coulomb waves thus obtained are highly symmetric with respect to signs of the energies and other constants of motion. It gives the precise phase shift for the continuum spectrum without any additive multiple of π in contrast to the existing solutions. The symmetry properties of the Dirac--Coulomb waves are discussed