The Nonrelativistic Limit

Abstract

In this chapter we analyze the behavior of the Dirac equation in the nonrelativistic limit and derive the explicit form of the first order relativistic correction. There are two main reasons for this investigation. The first is purely conceptual: It is important to see how the relativistic theory contains the successful nonrelativistic theory as a limiting case. The second reason is a practical one: In some cases it is useful to replace the Dirac theory by the much simpler Schrödinger theory together with some relativistic corrections. The first order corrections can sometimes be calculated explicitly, but it is not always necessary and is often impossible to calculate higher order corrections or the exact solution of the Dirac equation. Besides, for a higher accuracy we expect quantum electrodynamical effects to play a certain role (e.g., the Lamb shift). These effects cannot be described by the Dirac equation alone.