# 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}=

**p**^{2}+

*m*

^{2}and on the quantum mechanical correspondence principle, i.e. the replacement of the momentum

*by the operator*

**p**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 *k*^{0} = ±*ω*(* k*) together (

*ω*(

*) = (*

**k**

**k**^{2}+

*m*

^{2})

^{1 / 2}),

The Klein-Gordon field is quantized by interpreting the coefficients *a*(* k*) and

*c*(

*) as creation and annihilation operators*

**k**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).

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