(adsbygoogle = window.adsbygoogle || []).push({}); Prove that exp[A].exp= exp[A+B] only if A and B commute.

1. The problem statement, all variables and given/known data

Prove that e^{A}.e^{B}= e^{(A+B)}only if A and B commute.

The attempt at a solution

I expanded both sides of the equation.

(1+A+A^{2}/2!...)(1+B+B^{2}/2!+..) = (1+(A+B)+(A+B)^{2}/2!+..)

Now how to proceed ?

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# Prove that exp[A].exp = exp[A+B] only if A and B commute.

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