Exact solution of the Dirac-Coulomb equation and its application to bound-state problems. I External fields

An exact treatment of relativistic effects in bound-state problems in hydrogenlike atoms is given. In this paper we discuss the Zeeman effect and the Stark effect for relativistically bound electrons in a Coulomb field. For the Zeeman effect, the exact solution obtained by Darwin is used, and results of Crubellier and Feneuille for the Breit-Margenau correction are obtained in a simple way. For the Stark effect, the solution of Wong and Yeh is used. The exact expression can be readily compared with that of the Pauli approximation, and all correction terms can be identified. In the following paper we discuss interaction of the bound electron with radiation in an exact relativistic way. In the evaluation of the radial $r^K$ matrix elements with $n^{\prime }\ne n$, we present a closed-form expression as a sum over three parameters, derived from the method of the generating function of Laguerre polynomials.