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Compute a commutator

  1. Sep 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the resul of [Jx Jy , Jz] where J is the angular momentum operator.
    Possible answers to this multiple chioce question are
    A) 0
    B) i ħ Jz
    C) i ħ Jz Jx
    D) i ħ Jx Jz
    E) i ħ Jx Jy

    2. Relevant equations
    [AB,C]=A [B,C]+[A,B] B
    [Ji , Jj]=i ħ εijk Jk where εijk is the Levi-Civita symbol

    3. The attempt at a solution
    First of all, I used the first formula in this way
    [Jx Jy , Jz]=Jx[Jy , Jz]+[Jx , Jz]Jy
    Second, I used the second formula to write
    Jx[Jy , Jz]+[Jx , Jz]Jy=i ħ(J2x-J2y)
    Now I am stuck here because this result is not listed in the possible answers.
     
    Last edited: Sep 23, 2016
  2. jcsd
  3. Sep 23, 2016 #2
    Your math is fine. Just remember that within those J's are pauli spin matrices. When those are squared they equal 1.
     
  4. Sep 23, 2016 #3
    Thanks DuckAmuck for the advice!
    That was helpful
     
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