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Hermitian Operators Question

  1. Sep 29, 2013 #1
    1. The problem statement, all variables and given/known data
    [A,B] = C and operators A,B,C are all hermitian show that C=0


    2. Relevant equations



    3. The attempt at a solution

    Since it is given that all operators are hermitian I know that A=A' B=B' and C=C' so i expanded it out to
    AB-BA=C
    A'B'-B'A'=C
    (BA)' - (AB)'=C


    I'm not real sure where I am supposed to go or what properties of hermitian operators I am supposed to used to show that AB=BA..any help would be appreciated thank
     
  2. jcsd
  3. Sep 29, 2013 #2

    vela

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    Going back to AB-BA=C, what is C' equal to? How does it compare to what you derived so far?
     
  4. Sep 29, 2013 #3
    So would I just treat C and C' as separate equations, equate them and show that it equals zero?

    ie:

    C'=AB-BA
    C=(BA)'-(AB)' and just use the fact that all the operators are hermitian?
     
  5. Sep 29, 2013 #4

    vela

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    Not exactly. You have C=AB-BA, so C' = (AB-BA)'. With a little algebra, you should be able to show that C' = -C.
     
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