# 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

editThe 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

editThe case

test