$$\frac{\text{d} \langle x \rangle}{\text{d} t}=\int x \frac{∂}{∂t}|\Psi|^2\text d x$$
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 $$\frac{\text{d} \langle x \rangle}{\text{d} t} =0$$?

Question

$$\frac{\text{d} \langle x \rangle}{\text{d} t}=\int x \frac{∂}{∂t}|\Psi|^2\text d x$$
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 $$\frac{\text{d} \langle x \rangle}{\text{d} t} =0$$?

anonymous · Answer

I think they should have put x(t).

anonymous · Answer

Probably because Psi is a function of t, which makes x a function of t.

unklerhaukus · Answer

$$\Psi(x,t)$$