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Homework Statement
I am supposed to show that the free Schrödinger Equation is NOT kovariant under Galilei Transformation.
Homework Equations
We learned in Lectures that the Galilei Transformation can be written as:
[itex]\vec{x'}=\hat{R}\vec{x}-\vec{a}-\vec{v}t[/itex] (1) or equivalently:
[itex]\vec{x}=\hat{R^{-1}}\left(\vec{x'}+\vec{a}+\vec{v}t\right)[/itex] (2)
3. The Attempt at a Solution
I have no problem with evaluating the LHS of the time dependent Schrödinger equation.
However I am not sure if the second part of this is needed or not correct.
[itex]\frac{\partial}{\partial x_i}=\sum_k \frac{\partial x'_k}{\partial x_i}\frac{\partial}{\partial x'_k}+\frac{\partial t}{\partial x_i}\frac{\partial}{\partial t}[/itex]