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

a, b are operators that commute with their commutator

(1) Show that f(x) = e^{xa}e^{xb}satisfies df/dx = (a + b + x[a,b])f

(2) use (1) to show that e^{a}e^{b}= e^{a+b}e^{(1/2)[a,b]}

2. Relevant equations

[a,[b,a]] = [b,[b,a]] = 0

3. The attempt at a solution

I tried a Taylor expansion but just got a mess.

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# Homework Help: Proof of exp(a)exp(b) = exp(a+b)exp(1/2 [a,b])

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