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Position and momentum commutators

  1. Nov 27, 2008 #1
    Can I write:

    [itex][\hat{p^2},\hat{x}]\hat{p} = \hat{p}[\hat{p^2}, \hat{x}] [/itex]

    in relation to position and momentum operators?
     
  2. jcsd
  3. Nov 28, 2008 #2

    malawi_glenn

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    What do you think? can you show that you can do it?

    I think this is a good exercise in commutator algebra for you :-)
     
  4. Nov 28, 2008 #3
    [itex]\hat{C}[\hat{A},\hat{B}]=\hat{C}\hat{A}\hat{B}-\hat{C}\hat{B}\hat{A} [/itex]
    [itex][\hat{A},\hat{B}]\hat{C}=\hat{A}\hat{B}\hat{C}-\hat{B}\hat{A}\hat{C} [/itex]
    These two can't be the same as they are operators and the order matters.
     
  5. Nov 28, 2008 #4

    malawi_glenn

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    hey come on, don't write the answer just like that
     
  6. Nov 28, 2008 #5
    I was just wondering if there was an identity for such an expression. (Looking at thesage's post, it was a silly assumption; i should have remembered that expansion!)

    It stems from trying to prove that [itex][\hat{H},\hat{x}\hat{p}] = [\hat{H},\hat{p}\hat{x}][/itex].

    I did get this proof in the end. I was going wrong by not writing out p_hat explicitly, hence were my original post came from.

    Thanks for your feedback,
    regards benabean.
     
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