Foundations of the Relativistic Theory of Atomic and Molecular Structure

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This chapter discusses the basics of the relativistic theory of atomic and molecular structure. The dominant role of the atomic nucleus in the isolated atom means that the directional dependence of the wave function can be handled algebraically, so that only the dependence on the radial coordinate need can be treated by numerical methods. An understanding of the analytic behavior of Eigen solutions of the Dirac operator is fundamental to the construction of a rigorous description of the relativistic quantum mechanics of atoms and molecules. One-particle models provide a remarkably good first approximation for many processes in atoms and it is no coincidence that most many-body theories are built from one-body wave functions. In quantum electrodynamics textbooks, plane wave solutions of Dirac's equation for non-interacting free electrons are the commonest building blocks. Because the theory only conserves total charge, but not the individual numbers of electrons and positrons, excitations producing electron-positron pairs will appear only as intermediate states in perturbation expansions in low energy processes. At higher energies, real pairs may be produced.