Hmm, the general equation I reached is:
( m1*w^2-2K . . . . K(1+exp(ika)) ) (Ax) = (0)
( K(1+exp(-ika)). . . . m2*w^2-2K ) (Ay) = (0)
That's meant to be a matrix equation with vectors, tried to put dots between terms to line things up right, but not sure how clear it'll come out. And w is omega and K is kappa. So what I have is like an eigenvalue equation, but I didn't put the omega onto the other side.
I found the values of omega at the BZ boundary to be square root(2K/m1) and square root(2K/m2).
Putting k=pi/a and omega = square root (2K/m1) makes all terms in the matrix 0. And putting k=pi/a and omega = square root (2K/m2) gives non-zero diagonal terms but zero off-diagonals. Which I guess can't be right...
Not sure if the matrix is wrong, if the values of omega at the boundary are wrong, or if I'm making a mistake after that. The matrix seems to work for the k=0 case...
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