The Klein–Gordon Equation

From the early works on the constitution of the atom made by pioneers like A. Sommerfeld[aut]Sommerfeld, Arnold Johannes Wilhelm, the need to formulate relativistic equations in the quantum realm—that is, to find, so to speak, the relativistic counterpart of the Schrödinger[aut]Schrödinger, Erwin equation—arose. In this chapter, we will delve into the primary attempts made to arrive at such an equation, discussing the interpretative challenges encountered. We will then explore the relativistic equation for the electron obtained by P.A.M. Dirac[aut]Dirac, Paul Adrien Maurice, along with its physical interpretation and its connection to spin, and the prediction stemming from this equation regarding the existence of antimatter. Finally, we will conclude by discussing the discovery in 1932 of two fundamental particle which marked the beginning of the discovery era of elementary particles: the positron, by C. Anderson[aut]Anderson, Carl David, and the neutron, by J. Chadwick[aut]Chadwick, James and E. Rutherford[aut]Rutherford, Ernest.