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e^{A}e^{B}=e^{A+B}e^{[A,B]/2}

where A,B are operators and [ , ] is the commutator. The QM book I am using states it as a fact without proof, but I would like to see how it is proved. I've muddled around with the series expansion, but can't get farther than a few term by term products which lead nowhere.

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# Product of two exponentials of different operators

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