Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    DrDu

    User Avatar
    Science Advisor

    If the operators A, B, C commute, you can reorder them like ordinary numbers and hence the factorization of the exponential holds.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Coherent states
  1. Coherent States (Replies: 7)

  2. Coherent states (Replies: 3)

  3. Coherent state (Replies: 9)

  4. Coherent States. (Replies: 3)

Loading...