The Klein-Gordon Equation. Relativistic Equation for Spinless Particles

Abstract

When Schrödinger developed his nonrelativistic wave equation, he also proposed a relativistic generalization. This equation, studied in greater detail by Klein and Gordon (whose name it now bears) can be immediately obtained from the relation (1.7.4) for a free particle,

$$p.p = m^2 c^2,$$

with the substitutions suggested by the correspondence principle,

$$p0 = \frac{1}{c}E \to i\hbar\partial _t ,\,\,\,P \to -i\hbar\nabla.$$