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

I'm trying to compute something of the form [tex]\langle \int_a^b{f(x) dx} \int_a^b{f(x)^{\dagger}dx} \rangle [/tex] where the dagger means complex conjugate and the brackets are ensemble average (f(x) is a statistical quantity). I'm supposed to use the relation that [tex] \langle f(x) f(x')^{\dagger} \rangle = c*\delta(f-f')[/tex] where c is some constant.

2. Relevant equations

[tex] \langle f(x) f(x')^{\dagger} \rangle = c*\delta(f-f')[/tex]

3. The attempt at a solution

I'm a bit perplexed. I have the function and its complex conjugate, but inside different integrals, which are being multiplied. And the ensemble average of a product isn't the same as the product of ensemble averages, either... is it? I'd be surprised.

I thought maybe I could multiply the entire quantity by an extra f dagger, then somehow use the relation, but it didn't really get me anywhere.

So I have no idea how to use the given relation. Can anyone help??

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# Homework Help: Strange product of integrals

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