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Commutators and cevi levita symbol

  1. Aug 23, 2015 #1
    image.jpg
    1. The problem statement, all variables and given/known data
    The problem statement can be seen in the picture i uploaded.

    2. Relevant equations
    -

    3. The attempt at a solution
    The attempt to the solution can be seen in the picture i uploaded.
    I reached to the A and i dont know how to proceed to the solution that is given below. How does the minus and δkj disappear?
    If i do the double summation on k and j I think that every term gets zero either because of εijk (levi-cevita) or δkj (kronecker)
     
  2. jcsd
  3. Aug 23, 2015 #2

    TSny

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    You used the index j twice: once for the index on x and then again as a dummy summation index when writing out the angular momentum in terms of the levi-civita symbol.
     
  4. Aug 23, 2015 #3
    I cant see why this is wrong ... :/
     
  5. Aug 23, 2015 #4
    Moreover , if i use , lets say the index m on x (not on x that comes from angular momentum , yes on x that is alone) , then i still have the minus on ih bar ... My solutions say that it should not be there ...
     
  6. Aug 23, 2015 #5
    image.jpg Ok i think i understand why i cant have the same index on these two .
    Moreover i think i found how i get rid of this minus ...
    I must use the fact that εijk=-εikj wright ?
    Is now the solution correct ? (Uploaded photo)
     
  7. Aug 23, 2015 #6

    TSny

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    Yes. That looks very good.
     
  8. Aug 23, 2015 #7
    Thank you very much for your help :D
     
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