A Wave Equation for Spin-½ Particles: The Dirac Equation

Abstract

We follow the historical approach of Dirac who, in 1928, searched for a relativistic covariant wave equation of the Schrödinger form

$$ ih{\textstyle{{\partial \psi } \over {\partial t}}} = H\psi $$

((2.1))

with positive definite probability density. At that time there were doubts concerning the Klein—Gordon equation, which did not yield such probability density [see (1.29)] . The charge density interpretation was not known at that time and would have made little physical sense, because π⁺ and π^- mesons as charged spin-0 particles had not yet been discovered.