Posted by Steve Simon on April 17, 2014, 3:51 pm, in reply to "Diatomic Chain at BZ Boundaries"
Your approach sounds correct, and it should work (it should not be a matrix full of zeros!) I think we might have done the similar case for the alternating chain in lecture. You have omega^2 V = M(k) V with V a vector and M(k) a matrix. You just need to find the eigenvectors! 
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