What is the Klein Gordon equation

Klein-Gordon equation

Klein-Gordon equation[n], the relativistic generalization of the free Schrödinger equation for a spinless particle of mass m. It is based on the relativistic energy formula E.2 = p2 + m2 and on the quantum mechanical correspondence principle, i.e. the replacement of the momentum p by the operator

and reads with it

applied to a wave function

.

The general solution of the Klein-Gordon equation consists of solutions to positive and negative energy k0 = ±ω(k) together (ω(k) = (k2+m2)1 / 2),



The Klein-Gordon field is quantized by interpreting the coefficients a(k) and c(k) as creation and annihilation operators

and

, which are the commutation relations



meet (all other commutators disappear) and with which one can find the Hilbert space for any number of particles of mass m can build. The importance of the Klein-Gordon equation lies above all in the fact that all relativistic wave fields must satisfy it (quantum field theory).