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I've been self teaching myself solid state physics by reading Ashcroft and Mermin. What confuses me is that for the wave function in the lattice is written as the fourier series of waves obeying the Born-Von Karman Boundary Conditions while the potenial is written as the fourier series of waves in the reciprocal lattice. Look on page 137 in Ashcroft and Mermin to see what I mean. Is there any difference in the wave vectors used in both fourier series. Actually two different summation indices are used (K for the wavefunction and q for the potential) I would think that since a wave is in the reciprocal lattice it should obey the Born-Von-Karman BC's. I'm just not getting a feel for how K and q are related. Thanks for any help.

Modey3

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