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Integration of the reciprocal lattice

  1. Aug 1, 2012 #1
    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?

    ∫d3x f(x)eiK.x = [itex]\sum[/itex] aG∫d3x ei(K+G).x = Ω[itex]\sum[/itex]aGδk,-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
     
  2. jcsd
  3. Aug 2, 2012 #2
    If k = -G, then the value in the exponential is zero, which means your integral reduces to the integral of just d^3x, which is going to result in the volume of the space over which the integration occurs.
     
  4. Aug 2, 2012 #3
    I see it now.

    Is there any significance to the fact that k=-G? That is, k is in the opposite direction of the reciprocal lattice vector G
     
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