Waveequation for relativistic particle

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

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

Thanks heaps
 

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What happens when you do that substitution? Because that's all that there is to it...
 
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haha, yes i realized that, I was trying to get the wave function instead of the wave equation, and thats why it was a bit hard to do like that in my head.

Thanks though :)
 
Mute
Homework Helper
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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.
 

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