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Simple spherical quantum mechanics question: r dot p

  1. Nov 3, 2015 #1
    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. jcsd
  3. Nov 6, 2015 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    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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