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A About Glauber's formula(or special Baker–Campbell–Hausdorff

  1. Jun 29, 2016 #1
    upload_2016-6-29_18-13-21.png
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    Hi, I dont understand how to use 51 get 66. Can you help me with that?
     
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  3. Jun 29, 2016 #2

    blue_leaf77

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    Make the following replacement: ##F(B) = e^{At}## and ##A=B##.
     
  4. Jun 29, 2016 #3
    ok if I replace F(B) = e^At then should it be [A,B](e^At)' ? how does the t come from? and what do you mean by A=B? also the order of commutator seems reversed shouldnt it be negative then?
    Sorry I am stupid.
     
  5. Jun 29, 2016 #4

    blue_leaf77

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    ##(e^{At})' = \frac{d}{dA}e^{At}##.

    Yes, the order is reversed on both sides of the equation. So there will be negative sign in each side and they can cancel out.
     
  6. Jun 29, 2016 #5
    oh I didn't pay attention on the order of the commutator on the right hand side. Thank you so much for the help and time. And sorry for bothering you again.
     
  7. Jun 29, 2016 #6

    blue_leaf77

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    No worry, it's not a big deal.
     
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