I want to prove this formula(adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^Ae^B = e^Be^Ae^{[A,B]}[/tex]

The only method I can come up with is expand the LHS, and try to move all the B's to the left of all the A's, but it is so complicated in this way. i.e.

[tex]e^Ae^B=\frac{A^n}{n!}\frac{B^m}{m!} = \frac{1}{n!m!}\Big(A^{n-1}BAB^{m-1} + A^{n-1}[A,B]B^{m-1} \Big)= \cdots[/tex]

Is there any good way of proof of this formula?

thanks in advance

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# Proof of a commutator algebra exp(A)exp(B)=exp(B)exp(A)exp([A,B])

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