The Dirac Equation

Abstract

Nonrelativistic quantum mechanics, which was developed in the previous chapters, is very successful when applied to problems like the hydrogen atom, where the typical velocity (speaking semiclassically) is small compared to c. (Recall v/c=β=α≅.1/ 137 in the ground state.) But even in this case, there are measurable (fine-structure) corrections of the order of (v/c)⁴ which have to be put in by hand. If these corrections are to emerge naturally and if relativistic systems (high-Z atoms, for example) are to be described well, it is clear that we need an equation for the electron that has relativity built into it from the start. Such an equation was discovered by Dirac. We study it here with the main goal of seeing the coherent emergence of several concepts that were introduced disjointly at various stages—the spin of the electron, its magnetic moment (g = 2), the spin-orbit, and other fine-structure corrections.