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Your prof is using slightly wrong words: the group is a Lie group of dimension 10, not order 10. A group's order is the number of its elements, which is here uncountably infinite. A group of order 10 is a finite group (and indeed there are only two possible groups with 10 elements). I'm not sure how much continuous group theory (Lie group) theory you have ...


In your derivation you've implicitly assumed that the wavefunction does not change its values when you go to the Galilean boosted frame. In other words, you've assumed $\psi'(x', t') = \psi \bigl(x(x',t'), t(x',t') \bigr)$. However, this isn't right. The wavefunction encodes information about a particle's momentum, so when you go to a different frame the ...

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