4 - The Dirac Equation

Summary

In the previous chapter we discussed the direct relativistic generalization of the Schrödinger theory of quantum mechanics. It was shown that this leads to the Klein—Gordon equation from which some fundamental physics follows. Spin does not appear in either the Schrödinger or the Klein—Gordon theory. Indeed, the Klein—Gordon equation is only appropriate for particles with spin zero. Most of the particles encountered in everyday life (not that one actually encounters many fundamental particles in everyday life) are not spin zero. The most common ones, the neutron, proton and electron, all have spin 1/2. In this chapter we find the equation to describe particles with spin 1/2 and explore its properties. From the title of this chapter you will not be surprised to learn that it is known as the Dirac equation. The Dirac equation is more general than anything that has gone before, and therefore cannot really be derived. Much of the rest of this book involves looking for solutions of the Dirac equation under various circumstances.

Although the Dirac equation cannot really be derived from anything learnt up to the present level, some plausibility arguments for its existence can be given and a couple of these are presented in the first section.