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Non-commuting operators

  1. May 3, 2005 #1
    How do you prove the following identity for non-commuting operators A and B?

    [[[A,B],B]A]=[B,[A,[A,B]]]
     
  2. jcsd
  3. May 3, 2005 #2
    Hello S.G.,

    you could first use the abbreviation C:= [A,B], so the equation
    looks better:

    [[[A,B],B]A]=[B,[A,[A,B]]]
    <=>
    [[C,B],A] = [B,[A,C]]

    Then use the definition of the commutator [Y,Z] = YZ-ZY
    and in the end, instead of C, use [A,B] again.
     
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