Jump to content

PlanetPhysics/Klein Gordon Equation 3

From Wikiversity

This is a contributed Topic.

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

test