Posted by Steve Simon on May 26, 2014, 7:54 pm, in reply to "Show that a "
Well, you generally know that you can write V(r) in terms of its fourier transform V(r) = int dk e^{i k x} V_k Now all you need to show is that V_k is nonzero only for k being a reciprocal lattice vector  and this is a result of the fact that V is periodic. Does that help? 
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