PlanetPhysics/Klein Gordon Equation 3
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The Klein-Gordon (KG) Scalar Relativistic Wave Equation[edit | edit source]
{\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[edit | edit source]
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[edit | edit source]
1.3. Relativistic invanance of the de Broglie relations[edit | edit source]
1.4. Relativistic energy-momentum relation of a free particle[edit | edit source]
1.5. Charge and current density[edit | edit source]
1.5.1. Charge and current density in the presence of an electromagnetic field[edit | edit source]
1.6. Nonrelativistic limit[edit | edit source]
1.7. The initial data problem[edit | edit source]
1.8. Indefiniteness of the sign of charge[edit | edit source]
1.9. Interaction with an external electromagnetic field[edit | edit source]
1.10. Fine structure constant[edit | edit source]
The case
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