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Another index notation question hopefully pretty easy

  1. Mar 20, 2009 #1
    How do I make sense of the index notation expression

    [tex]
    r_j r_i p_j
    [/tex]

    ?

    What I really *want* it to be is

    [tex]
    \vec{r} (\vec{r} \cdot \vec{p})
    [/tex]

    And it turns into this, as long as I can commute the [itex]r_i[/tex] and [itex]r_j[/itex]...right?

    (By the way, here [itex]\vec{r}[/itex] is just the position vector and [itex]\vec{p}[/itex] is the momentum vector.)
     
  2. jcsd
  3. Mar 20, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, those are simply coordinates, i.e. numbers, so they are commutative, aren't they?
     
  4. Mar 20, 2009 #3
    Yes, you can commute them just fine. I know how you feel, after doing a lot of quantum operator calculations it feels like such a breeze to have the commutative property!
     
  5. Mar 21, 2009 #4
    Thanks guys! Yes, this is actually something that's come up in trying to solve a quantum problem. And yeah...I've done enough of these to where I pretty much don't believe anything commutes anymore :(
     
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