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

  • #1
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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?
 

Answers and Replies

  • #2
blue_leaf77
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Make the following replacement: ##F(B) = e^{At}## and ##A=B##.
 
  • #3
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Make the following replacement: ##F(B) = e^{At}## and ##A=B##.
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.
 
  • #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.
 
  • #5
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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.
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.
 
  • #6
blue_leaf77
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No worry, it's not a big deal.
 
  • #7
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Which book is this from?
 
  • #8
dextercioby
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C. Cohen-Tannoudji et al. - Quantum Mechanics.
 
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