Paul Dirac formulated the relativistic wave equation for the electron in 1928.
The Dirac equation combined quantum mechanics with special relativity while describing particles with spin one-half. It naturally accounted for the electron’s spin and magnetic moment and predicted the existence of corresponding antiparticles. The positron, the electron’s antiparticle, was discovered by Carl Anderson in 1932, providing striking support for Dirac’s prediction.
Dirac’s equation uses four-component spinors rather than the single-component wavefunction of the basic nonrelativistic Schrödinger equation. Its structure also leads to the correct relativistic energy relationship for a free spin-half particle. The equation is not a complete theory of interacting electrons and photons; that role belongs to quantum electrodynamics. Dirac shared the 1933 Nobel Prize in Physics with Schrödinger for discoveries concerning atomic theory.