A Wave Equation for Spin-1/2 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

$$ i\hbar \frac{{\partial \psi }} {{\partial t}} = \hat H\psi $$

(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.