Waveequation for relativistic particle

[salaric]

How do I find the wave equation for a relativistic particle from E and p in terms of their operator-equations, E \leftrightarrow i \hbar \frac{d}{dt} and p \leftrightarrow - i \hbar \frac{d}{dx} ?

I'm assuming I'll have to use: E^{2}=p^{2}c^{2}+\left(m_{0}c^{2}\right)^{2}
and substitude the operator-equations into that, but where to go from there? I'm lost.

Thanks heaps

 

[lbrits]

What happens when you do that substitution? Because that's all that there is to it...

 

[salaric]

haha, yes i realized that, I was trying to get the wave function instead of the wave equation, and that's why it was a bit hard to do like that in my head.

Thanks though :)

 

[Mute]

http://en.wikipedia.org/wiki/Klein-Gordon_equation

This is basically what you're trying to get at, right? Note that this isn't the relativistic wave equation used in QFT - that's the dirac equation - since this equation doesn't incorporate spin.