The Motion of a Dirac Electron in a Magnetic Field

Abstract

Solutions of the Dirac wave equation representing a free electron moving in a uniform magnetic field are obtained. The functions are similar to those obtained by Landau and by Uhlenbeck and Young as solutions of the Schrödinger equation. A wave packet is constructed representing a beam of electrons passing through a slit. The results agree with the classical predictions to terms of the order of the de Broglie wave-length of the electron divided by the radius of curvature of its classical path. For experimental cases this ratio is of the order ${10}^{-8\mathrm{}}$ to ${10}^{-10\mathrm{}}$. Hence it is concluded that the difference between magnetic deflection measurements of $\frac{e}{m}$ and other determinations cannot be explained as a quantum effect.