Simple spherical quantum mechanics question: r dot p

[zhaos]

Homework Statement

Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/...all-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see

$$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$

Where ##r## is the radial distance. Why is this relation true?

Homework Equations

$$ \vec{\nabla_r} = (\frac{\partial}{\partial r}, \frac{1}{r}\frac{\partial}{\partial \theta}, \frac{1}{r \sin \theta}\frac{\partial}{\partial \phi}) $$

The Attempt at a Solution

So is ##\vec{r}\cdot\vec{p}## simply

$$ (r, 0, 0) \cdot -i\hbar\vec{\nabla_r} = -i\hbar r \frac{\partial}{\partial r} $$

??

 

[Simon Bridge]

Well done.
You should verify by context... is this consistent with what the notes and documents are trying to tell you?