Simple spherical quantum mechanics question: r dot p

1. Nov 3, 2015

zhaos

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

3. The attempt at a solution
So is $\vec{r}\cdot\vec{p}$ simply

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

??

2. Nov 6, 2015

Simon Bridge

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

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