The Dirac Hydrogen Atom

The simplest system of relevance for molecular sciences is the hydrogen atom. The quantum mechanical equation of motion for an electron in the attractive (external) potential of a positively charged atomic nucleus can be solved analytically. From these analytical results many important consequences follow, which make the description of many-electron atoms and molecules feasible. This chapter investigates how angular momentum enters the Dirac equation for hydrogen-like atoms. Before investigating in more detail the eigenpairs of the Dirac equation for hydrogen-like atoms, that is, the energy eigenvalue and the corresponding set of radial functions, the chapter looks into the relation of the Dirac and Schrödinger hydrogen atoms. The chapter also discusses some important properties such as the number of nodes and the energy eigenvalues.