On the discrete solutions of Dirac radial equations system for hydrogen atom

Full text: The question of the Dirac theory conformation with the non-relativistic quantum mechanics of the Hydrogen atom is somewhat nontrivial. However the necessity of this conformation is a natural requirement of the accordance principle. One may naturally suppose that the important notion of the principal quantum number has to figurate in the Dirac theory for example. The notion of the principal quantum number may be introduced into Dirac relativistic theory in a successive way indeed. When it is done one may discover not well known particularities of the Dirac radial equation system's eigenvalues and eigenfunctions discrete spectrum as well as quite unknown particularities. One may result the careful investigation of these particularities in a form of three Statements, which are autonomous and independent one from another. However the joint of them gives some imagination about complicated character of the total energy eigenvalues discrete spectrum and the corresponding eigenfunctions for the Hydrogen atom. The Statement's differences are conditioned, first, by existence of two subsystems in the four Dirac radial equations system; second, by differences in possible combinations of two discrete numbers - the principal quantum number and the angular momentum quantum number; and third, by differences in the Statement proving ways. The last one is caused by specifics of the corresponding differential equations. From the point of view of the existence of these distinctions it becomes obvious that actually the well known Sommerfeld formula is in fact a formal combination of three essentially different formulas with different origins. In other words, the nature of emission and absorption spectral line fine splitting in Hydrogen atom displays greater complication in comparison with the traditional imagination about it