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

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Hi, I dont understand how to use 51 get 66. Can you help me with that?
 

blue_leaf77

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Make the following replacement: ##F(B) = e^{At}## and ##A=B##.
 
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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.
 

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.
 
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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.
 

blue_leaf77

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No worry, it's not a big deal.
 
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Which book is this from?
 

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