I am working on the Hydrogen atom and I was trying to calculate [tex]\frac{d<r>}{dt}[/tex] using [tex]\frac{d<r>}{dt} = \frac{i}{\hbar} <[\hat{H} , \hat{r}]>[/tex]. Here [tex]r = \sqrt(x^2 + y^2 + z^2)[/tex] and [tex]H = \frac{p^2}{2m} + V[/tex] where [tex]p^2 = -\hbar^2 \nabla^2 [/tex]. Now according to Ehrenfest's theorem <r> should behave classically and give me some equivalent of velocity, and indeed I do get something but it does't resemble velocity: [tex]\frac{-\hbar^2}{2m} (2\nabla r \nabla f + f \nabla^2 r)[/tex]



where f is a test function.



Am I doing something wrong?