Normal coordinate substitutions with periodic boundary conditions

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This discussion focuses on normal coordinate substitutions in the context of periodic boundary conditions, specifically addressing the cancellation of the 1/N factor. Doug inquires about the mathematical derivation, referencing the equation involving the summation of exponentials, which simplifies to N when k equals k'. This indicates that the normalization factor is inherently tied to the number of terms in the sum, reinforcing the importance of understanding periodic boundary conditions in this context.

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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
 

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Probably:
[tex]\sum_{k} e^{i (k - k') a} = N \delta_{k,k'}[/tex]

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

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