PlanetPhysics/Klein Gordon Equation 3

This is a contributed Topic.

The Klein-Gordon (KG) Scalar Relativistic Wave Equation edit

{\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

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

1.3. Relativistic invanance of the de Broglie relations edit

1.4. Relativistic energy-momentum relation of a free particle edit

1.5. Charge and current density edit

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

1.6. Nonrelativistic limit edit

1.7. The initial data problem edit

1.8. Indefiniteness of the sign of charge edit

1.9. Interaction with an external electromagnetic field edit

1.10. Fine structure constant edit

The case  

test