PlanetPhysics/Klein Gordon Equation

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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.


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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: