Posted by Steve Simon on May 7, 2013, 9:43 am, in reply to "Re: Normal modes of diatomic chain"
Sorry, I didn't realize I left this unanswered!! You could include such a factor if you wanted to, but you would get the same frequencies. Instead of having A_1 e^{i k n a  i omega t} and A_2 e^{i k n a  i omega t} You would have A_1 e^{i k n a  i omega t} and A_2 e^{i k (n + 1/2) a  i omega t} But this just amounts to redefining A_2 to include an additional phase of e^{ika/2}. 
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