Hymne
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Hello! Hopefully somebody could give me a push from behind on this one :)
Show that the classical wave equation is lorentz invariant.
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<br /> <br /> \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..
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<br /> <br /> \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..