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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