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I Commutator Properties

  1. Dec 16, 2016 #1
    Given the property,

    [A,BC] = [A,B]C+B[A,C],

    is it true that, if B=C, then

    [A,B]C+B[A,C]=[A,B]C+B[A,B]=[A,B](C+B)?

    I apologize if I have posted in the wrong forum.
     
  2. jcsd
  3. Dec 16, 2016 #2

    fresh_42

    Staff: Mentor

    The commutator (in the assumed context above) is defined as ##[A,B]=AB-BA##.
    Now you have ##[A,B]C+B[A,C]=[A,B]B+B[A,B]=AB^2-B^2A## on the left and a factor ##2## on the right.
    The (presumably) operators (or linear mappings) ##A,B,C## do not commutate, so you cannot switch orders.
     
  4. Dec 16, 2016 #3
    Thank you for your help. I understand now.
     
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