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Need help with index notation.

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove the following:
    [tex](\vec{r}\times\nabla)\cdot(\vec{r}\times\nabla)=r^2\nabla^2-r^2 \frac{\partial^2}{\partial r^2}-2r\frac{\partial}{\partial r}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    At this point, I'm lost. Does the gradient operator work on all terms, should I rearrange?
  2. jcsd
  3. Sep 17, 2010 #2


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    Homework Helper

    One of your equations is wrong,
    I personally would write:
    \mathbf{r}=x_{i}\hat{e}_{i},\quad\nabla =\hat{e}_{i}\partial_{i}
    Hopefully this should help.

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