- #1

cartonn30gel

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## Homework Statement

I'm trying to show that the wave equation is not invariant under Galilean transform. To do that I need to figure out how the Laplacian transforms from S to S'. I seem to have trouble understanding why the laplacian actually changes.

## Homework Equations

x'=x-vt, t'=t

## The Attempt at a Solution

Just consider the second derivative wrt x in cartesian coordinates:

[tex]\frac{\partial^2}{\partial x'^2}=\frac{\partial}{\partial x'} \frac{\partial}{\partial x'} = (\frac{\partial x}{\partial x'} \frac{\partial}{\partial x}) (\frac{\partial x}{\partial x'} \frac{\partial}{\partial x}) = \frac{\partial}{\partial x} \frac{\partial}{\partial x} = \frac{\partial^2}{\partial x^2}[/tex]

So if you do the same for all three components, it looks like the Laplacian just transforms as it is. But I know that this is not right. Any help??

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