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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