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QM: Product expectation value

  1. Jul 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi

    I have read a paper, where they want to find the average number of photons in a cavity. They have an expression for [itex]\langle{\hat a}\rangle[/itex], and then they use
    [tex]
    \langle{\hat a}\rangle^* = \langle{\hat a^\dagger}\rangle
    [/tex]
    to find [itex]\langle{\hat a^\dagger \hat a}\rangle[/itex]. I agree with the above relation, however what I don't agree with is the following equality
    [tex]
    \langle{\hat a^\dagger \hat a}\rangle = \langle{\hat a}\rangle^*\langle{\hat a}\rangle
    [/tex]
    Am I right? I mean, one can't just factorize an expectation value like that.

    Best,
    Niles.
     
  2. jcsd
  3. Jul 29, 2012 #2
    You are right in that the equality doesn't hold in general. It is a commonly made approximation in order to "close" the set of correlation functions.
     
  4. Jul 29, 2012 #3
    Thanks! I read it here, on page 12/13, where they do as I wrote in my OP: http://mediatum2.ub.tum.de/doc/652711/652711.pdf

    I can't see however why the approximation is valid in this case.
     
  5. Jul 31, 2012 #4
    If I'm not mistaken the equality holds because the authors are considering the steady state case.
     
  6. Jul 31, 2012 #5
    It is not obvious to me why it should be valid in steady state.
     
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