On the relation between the eigenvalues in relativistic and non-relativistic quantum mechanics

The object of the paper is to apply rigorous analysis to the problem of treating Dirac’s relativistic equations in quantum mechanics as a perturbed form of Schrodinger’s equation, with small perturbation parameter c-1, where c is the velocity of light. It is proved that in certain cases the perturbed eigenvalues and eigenfunctions can be expanded in convergent series of inverse powers of c. The well-known case of the hydrogen atom is a simple example.