PlanetPhysics/Klein Gordon Equation 3

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The Klein-Gordon (KG) Scalar Relativistic Wave Equation

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{\mathbf Remarks:} The KG-equation is a Lorentz invariant expression. For specific computations of specific cases it can only be utilized with the appropriate boundary conditions.

1.1. The Klein-Gordon equation

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

 

Here the   symbol refers to the wave operator, or D'Alembertian, ( ) and   is the wave function of a spinless particle.

1.2. Relativistic energy levels of a spinless particle in a Coulomb field

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1.3. Relativistic invanance of the de Broglie relations

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1.4. Relativistic energy-momentum relation of a free particle

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1.5. Charge and current density

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1.5.1. Charge and current density in the presence of an electromagnetic field

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1.6. Nonrelativistic limit

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1.7. The initial data problem

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1.8. Indefiniteness of the sign of charge

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1.9. Interaction with an external electromagnetic field

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1.10. Fine structure constant

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The case  

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