Question

\[\frac{\text{d} \langle x \rangle}{\text{d} t}=\int x \frac{∂}{∂x}|\Psi|^2\text d x\]
Why can't you do integration-by-parts of the expression on the right- pull the time derivative over onto x , note that ∂x/∂t =0 and conclude that \[\frac{\text{d} \langle x \rangle}{\text{d} t} =0\]?

Answer 1

typo*

Answer 2

should be
\[\frac{\text{d} \langle x \rangle}{\text{d} t}=\int x \frac{∂}{∂t}|\Psi|^2\text d x\]