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Coherent states

  1. May 6, 2015 #1
    Look at the following attached picture, where they prove the coherent states are eigenfunctions of the annihiliation operators by simply proving aexp(φa)l0> = φexp(φa)l0>. I understand the proof but does that also prove that:
    aiexp(Σφiai)l0> = φiexp(Σφiai)l0> ?
    I can see that it would if you can use that:
    exp(A+B+...) = exp(A)exp(B)exp(C)...
    but does that identity hold for operators and how do you see that?
    Because if you just taylor expand the operator sum you get cross terms between i and j and I'm not sure what to do with these.
    Edit: the picture might be a bit too small, so you can also just look at p158-159 of http://nanotheoryou.wikispaces.com/file/view/Atland+And+Simons.pdf

    Attached Files:

  2. jcsd
  3. May 6, 2015 #2


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    Science Advisor

    If the operators A, B, C commute, you can reorder them like ordinary numbers and hence the factorization of the exponential holds.
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