An equation in relativistic quantum mechanics for spin-zero particles. The Klein–Gordon equation has the form
[☐ − (mc/ħ)2]ψ = 0,
where ☐ = ∇2 − (1/c2)(∂/∂t2), and ∇2 is the Laplace operator (see Laplace equation), m is the mass of the particle, c is the speed of light, ħ is the Dirac constant (see Planck constant), and ψ is the wave function of the particle. This equation was discovered by several authors independently, including the Swedish physicist Oskar Klein (1894–1977) and Walter Gordon (1893–1940) in 1926. The Klein–Gordon equation is not viable as an equation in single-particle relativistic quantum mechanics but does describe spin-zero particles, such as mesons; it includes the prediction of the existence of antiparticles for such particles. See also Dirac equation.