The Dirac Electron in Simple Fields

Abstract

The relativity wave equations for the Dirac electron are transformed in a simple manner into a symmetric canonical form. This canonical form makes readily possible the investigation of the characteristics of the solutions of these relativity equations for simple potential fields. If the potential is a polynomial of any degree in $x$, a continuous energy spectrum characterizes the solutions. If the potential is a polynomial of any degree in $\frac{1}{x}$, the solutions possess a continuous energy spectrum when the energy is numerically greater than the rest-energy of the electron; values of the energy numerically less than the rest-energy are barred. When the potential is a polynomial of any degree in $r$, all values of the energy are allowed. For potentials which are polynomials in $\frac{1}{r}$ of degree higher than the first, the energy spectrum is again continuous. The quantization arising for the Coulomb potential is an exceptional case.