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I've been spending a lot of time trying to solve this problem but I can't figure out a good solution.

I have to show that the action of a non-relativistic particle ( Schrodinger density Lagrangian ) is invariant under Galilean boost with the form

ψ(x_{0},x)→ψ'(x_{0},x)=e^{imvx-(im/2)x0v2}ψ(x_{0},x-vx_{0})

x_{0}= t

I've tried to find the transformed Lagrangian by replacing the wave functions and the derivatives but I'm not sure I did it correctly because I get monstrous expressions

I'm using this density Lagrangian L= ihψ*[itex]\partial[/itex]_{0}ψ+h^{2}/2m([itex]\partial[/itex]_{i}ψ*)([itex]\partial[/itex]_{i}ψ)

If someone can give me a good tip I'll appreciate it

thank you!

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# Action invariance under galilean boost

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