# PlanetPhysics/Klein Gordon Equation

The Klein-Gordon equation is an equation of mathematical physics that describes spin-0 particles. It is given by:

Here the symbol refers to the wave operator, or D'Alembertian, and is the wavefunction of a particle. It is a Lorentz invariant expression.

### Derivation

[edit | edit source]Like the Dirac equation, the Klein-Gordon equation is derived from the relativistic expression for total energy:

Instead of taking the square root (as Dirac did), we keep the equation in squared form and replace the momentum and energy with their operator equivalents, , . This gives (in disembodied operator form)

Rearranging:

Dividing both sides by :

Identifying the expression in brackets as the D'Alembertian and right-multiplying the whole expression by , we obtain the Klein-Gordon equation: