In a discussion of the second order transitions in graphene this mathematical expression is used. $$ \left|\frac{1}{\varepsilon + i \Gamma/2}\right|^2 = \frac{2\pi}{\Gamma}\delta(\epsilon) $$ And I'm kind of confused right now. Can someone prove this equation?

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    $\begingroup$ Which discussion? $\endgroup$ – Emilio Pisanty Apr 17 '19 at 8:26
  • $\begingroup$ It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts. $\endgroup$ – Levon Apr 17 '19 at 8:38
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    $\begingroup$ No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about. $\endgroup$ – Emilio Pisanty Apr 17 '19 at 9:32

OP's formula is derived from the Poisson kernel representation $$ \delta(\varepsilon)~=~\lim_{\Gamma \to 0^+}\frac{1}{\pi}\frac{\Gamma/2}{|\varepsilon+i\Gamma/2|^2} $$ of the Dirac delta distribution.


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