Klein-Gordon equation
The Klein-Gordon equation is an equation of mathematical physics that describes 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 particle. It is a Lorentz invariant expression.
0.1 Derivation
Like the Dirac equation, the Klein-Gordon equation is derived from the relativistic expression for total energy:
Instead of taking the square root (as Dirac did), we keep the equation in squared form and replace the momentum and energy with their operator equivalents, , . This gives (in disembodied operator form)
Rearranging:
Dividing both sides by :
Identifying the expression in brackets as the D’Alembertian and right-multiplying the whole expression by , we obtain the Klein-Gordon equation:
Title | Klein-Gordon equation |
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Canonical name | KleinGordonEquation |
Date of creation | 2013-03-22 17:55:11 |
Last modified on | 2013-03-22 17:55:11 |
Owner | invisiblerhino (19637) |
Last modified by | invisiblerhino (19637) |
Numerical id | 12 |
Author | invisiblerhino (19637) |
Entry type | Definition |
Classification | msc 78A25 |
Classification | msc 35Q60 |
Synonym | Klein Gordon equation |
Synonym | Klein-Gordon-Fock equation |
Related topic | DiracEquation |
Related topic | SchrodingersWaveEquation |