Posted by Steve Simon on February 24, 2014, 5:20 pm, in reply to "Normal modes of a 1D Chain"
Yes, you need them both!
In the reduced zone scheme you need to get two modes per value of k (between k=-pi/a and pi/a) so that when you unfold this to extended zone scheme you have one mode per k for k between k=-2 pi/a and 2pi/a. Note that his second range is the BZ for the 1d monatomic chain with lattice constant a/2. When you consider the monatomic chain you should get a dispersion omega ~ |sin(k a/4)| which is the right dispersion for a monatomic chain with lattice constant a/2. If you then fold this back up to the reduced zone scheme for the diatomic chain you need to get two modes per k and one will look like sin and the other like cos. (What else could you get from folding over a sin?)
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