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Lorentz invariance of wave eqn.

  • Thread starter Hymne
  • Start date
  • #1
89
0
Hello! Hopefully somebody could give me a push from behind on this one :)

Homework Statement



Show that the classical wave equation is lorentz invariant.


The Attempt at a Solution


I tried to exchange all derivatives by the chain rule:

[tex] (c^2 \frac{d^2 }{dt^2} + \frac{d^2 }{dx^2} + \frac{d^2 }{dy^2} + \frac{d^2 }{dz^2}) \phi = 0 ; \quad

\frac{d}{dx} \rightarrow \frac{d}{dx}\frac{dx}{dx'}[/tex]
And the same for the time derivative and use lorentz transformation. But somewhere it goes wrong..
 

Answers and Replies

  • #2
121
4
I'd just substitute in the transformed coordinates and boil it all back down to what it started as. Not sure I'd use the chain rule explicitly.

Adrian.
 

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