Klein–Gordon equation | Wikipedia audio article
Channel: wikipedia tts
Date: 24/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation


00:02:09 1 Statement
00:07:41 2 History
00:10:05 3 Derivation
00:19:51 3.1 Klein–Gordon equation in a potential
00:20:25 4 Conserved current
00:21:49 5 Relativistic free particle solution
00:25:36 6 Action
00:28:39 7 Electromagnetic interaction
00:34:09 8 Gravitational interaction
00:37:08 9 See also
00:37:31 10 Remarks



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SUMMARY
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The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second order in space and time and manifestly Lorentz covariant. It is a quantized version of the relativistic energy–momentum relation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Its theoretical relevance is similar to that of the Dirac equation. Electromagnetic interactions can be incorporated, forming the topic of scalar electrodynamics, but because common spinless particles like the pi mesons are unstable and also experience the strong interaction (with unknown interaction term in the Hamiltonian), the practical utility is limited.
The equation can be put into the form of a Schrödinger equation. In this form it is expressed as two coupled differential equations, each of first order in time. The solutions have two components, reflecting the charge degree of freedom in relativity. It admits a conserved quantity, but this is not positive definite. The wave function cannot therefore be interpreted as a probability amplitude. The conserved quantity is instead interpreted as electric charge and the norm squared of the wave function is interpreted as a charge density. The equation describes all spinless particles with positive, negative as well as zero charge. 
Any solution of the free Dirac equation is, component-wise, a solution of the free Klein–Gordon equation.
The equation does not form the basis of a consistent quantum relativistic one-particle theory. There is no known such theory for particles of any spin. For full reconciliation of quantum mechanics with special relativity quantum field theory is needed, in which the Klein–Gordon equation reemerges as the equation obeyed by the components of all free quantum fields. In quantum field theory, the solutions of the free (noninteracting) versions of the original equations still play a role. They are needed to build the Hilbert space (Fock space) and to express quantum field by using complete sets (spanning sets of Hilbert space) of wave functions.