I am studying Solid state physics from kittel and I am stuck at the following equation. I can see that the exponential term turns to the kroneckler delta, but I dont understand how the integral gives the volume of the specimen, Ω? What am I not seeing?(adsbygoogle = window.adsbygoogle || []).push({});

∫d^{3}x f(x)e^{iK.x}= [itex]\sum[/itex] a_{G}∫d^{3}x e^{i(K+G).x}= Ω[itex]\sum[/itex]a_{G}δ_{k,-G}

f(x) is the fourier transform of the lattice, ie. the reciprocal lattice and he wants to prove that integration is not zero unless k is a vector in the reciprocal lattice G

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# Integration of the reciprocal lattice

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