RELATIVISTIC HYDROGEN-ATOM IN A STRONG MAGNETIC-FIELD

Dirac's equation of the hydrogen atom in a strong magnetic field is transformed to an infinite set of ordinary differential equations by expanding each component of the electron spinor in terms of the Landau orbitals. In the vanishing limit of the fine-structure constant, alpha to 0, the set of equations correctly reduces to the previously used non-relativistic form. The adiabatic approximation is introduced as an extension to finite fields of the form of the equations in the infinite magnetic field strength limit. The results of the numerical integration of the adiabatic equations are presented. The ground state experiences only a minor relativistic correction, but for the magnetically excited states the correction becomes prominent with increasing field strengths.