Evaluating Some Relativistic One-Electron Atomic Properties with Mathematica

The literature contains several analytic or semianalytic formulas that can be used to calculate some simple properties and various decay rates of the relativistic hydrogenic atom. To date, all of these formulas depend on two-component atomic wavefunctions. In this paper we derive the necessary working formulas needed to evaluate some simple properties and the decay rate for M1, E1, E2 or M2 transitions with a four-component wavefunction. We also show that both methods yield identical results.