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Why do Galilean transformations change both states and operators?
When a Galilean transformation on a quantum system is performed, the states and the operators change:
$$|\phi\rangle \rightarrow |\phi\rangle'$$
$$\hat A \rightarrow \hat A'$$
I don't understand the ...
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Why the Galileo transformation are written like this in Quantum Mechanics?
In Quantum Mechanics it is said that the Galileo transformation $$\hat{\mathbf{r}}\mapsto \hat{\mathbf{r}}-\mathbf{v}t\quad \text{and}\quad \hat{\mathbf{p}}\mapsto \hat{\mathbf{p}}-m\mathbf{v}\tag{1}...
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