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

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)




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: