Normal coordinate substitutions with periodic boundary conditions

[phdojg]

Could someone plase hep me with normal coordinate substitutions with periodic boundary conditions, I can't see where the 1/N cancels in the attached file

Thanks

Doug

 

[CompuChip]

Probably:
$$\sum_{k} e^{i (k - k') a} = N \delta_{k,k'}$$

(If k = k' then you have the sum over 1, so you get the number of terms N).