(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume C=[A,B]≠0 and [C,A]=[C,B]=0

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e^{A}e^{B}=e^{A+B}e^{[itex]\frac{1}{2}[/itex][A,B]}

2. Relevant equations

All are given above.

3. The attempt at a solution

I recently did a similar problem (show e^{A}Be^{-A}= B + [A,B] + [itex]\frac{1}{2}[/itex][A,[A,b]]+...) by defining a function e^{xA}Be^{-xA}and doing a taylor expansion, so I thought this might be done similarly, but I have gotten nowhere with this approach. I would like to figure this out myself, so I am really looking for guidance/hints if anyone has any. It would be much appreciated

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# Homework Help: A proof of operators in exponentials

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