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Homework Statement
If A and B are two operators such that
[A,B] = λ , where l is a complex number, and
if μis a second complex number, show that:
exp[μ(A + B)] = exp(μA)exp(μB)exp(- λμ^2/ 2).
Homework Equations
The Attempt at a Solution
I'm stuck on where to begin. I know that the result [x, p_x] = ih_bar indicates that x and p_x relate by the uncertainty principle. I'm not sure if this conclusion applies to complex commutators in general.
Also, I don't understand the significance of the exponential function. Do I lose anything by expressing that information as
μ(A+B)=(-λμ^2)/2 ?
Any ideas?
Thanks