For the Golden Rule cross-section function, there is a factor $2pi$ in every delta function and a factor of $1/2pi$ for every derivative. Any easy and intuitive way to understand such factors?
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Hint: it's all because the inverse of the Fourier transform $\tilde{f}(k)=\int_{\Bbb R^n}f(x)e^{-ik\cdot x}d^nx$ is $f(x)=(2\pi)^{-n}\int_{\Bbb R^n}\tilde{f}(k)e^{ik\cdot x}d^nk$. – J.G. Oct 20 '22 at 13:53
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Many thank! But what about the $2\pi$ for each delta function? – liu yang Oct 25 '22 at 01:56
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Well, that the inverse works that way is equivalent to $\int_{\Bbb R^n}e^{ik\cdot x}d^nx=(2\pi)^n\delta^n(k)$. – J.G. Oct 25 '22 at 07:12