Klein gordon equation

**ppyvabw** · May 15th 2008, 09:57 AM

I am being really thick here

I have this wave equation, the massless klien gordon equation

$\partial_{\mu}\partial^{\mu}\phi(x)=0$

where the summation over $\mu$ is over 0,1,2,3

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

$\phi(x)=\int d^4 p \overline{\phi}(p)exp(i p_{\mu}x^{\mu})$

where $\overline{\phi}$ is the weighting function.

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

$p_{\mu}p^{\mu}$ which equals zero. (mass shell constraint)

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

Hope peeps understand the question.

**mr fantastic** · May 16th 2008, 03:38 AM

Originally Posted by ppyvabw

I am being really thick here

I have this wave equation, the massless klien gordon equation

$\partial_{\mu}\partial^{\mu}\phi(x)=0$

where the summation over $\mu$ is over 0,1,2,3

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

$\phi(x)=\int d^4 p \overline{\phi}(p)exp(i p_{\mu}x^{\mu})$

where $\overline{\phi}$ is the weighting function.

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

$p_{\mu}p^{\mu}$ which equals zero. (mass shell constraint)

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

Hope peeps understand the question.

The K-G equation is linear and plane waves (with the mass shell constraint) are solutions to it. Therefore arbitrary linear combinations of plane waves are solutions to it. Therefore $\overline{\phi}(p)$ is arbitary.

Thread: Klein gordon equation

LinkBack

Thread Tools

Display

Klein gordon equation

Similar Math Help Forum Discussions

Klein Bottle Covering

Isomorphism: Klein 4 and Z2 x Z2

Klein Four Group

Klein 4-group

Klein four-group is no cyclic

Search Tags