I am being really thick here(adsbygoogle = window.adsbygoogle || []).push({});

I have this wave equation, the massless klien gordon equation

[tex]\partial_{\mu}\partial^{\mu}\phi(x)=0[/tex]

where the summation over [tex]\mu[/tex] is over 0,1,2,3

the general solution is a superposition of plane waves yes? i.e

[tex]\phi(x)=\int d^4 p \overline{\phi}(p)exp(i p_{\mu}x^{\mu})[/tex]

where [tex]\overline{\phi}[/tex] is the weighting function.

When you susbsitute this back into the klein gordon equation you get down two factors of p, i.e

[tex]p_{\mu}p^{\mu}[/tex] which equals zero. (mass shell constraint), thus satisfying the equation of motion.

My question is, is [tex]\overline{\phi}(p)[/tex] arbitrary? I don't really understand why this is so, let alone believe it.

Hope peeps understand the question.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Klein gordon equation

Loading...

Similar Threads for Klein gordon equation |
---|

A Coulomb Klein Gordon: Where does e^(-iEt) come from? |

I Negative and Positive energy modes of KG equation |

A The Lagrangian Density and Equations of Motion |

I Klein-Gordon propagator derivation |

**Physics Forums | Science Articles, Homework Help, Discussion**