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

#### Frost_Xue

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

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#### blue_leaf77

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

#### Frost_Xue

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

Homework Helper
$(e^{At})' = \frac{d}{dA}e^{At}$.

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.

#### Frost_Xue

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

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

Homework Helper
No worry, it's not a big deal.

#### annaphys

Which book is this from?