B An Important Lattice Sum

Applying periodic boundary conditions, we have, according to (2.34), eiq Na and therefore 

C) Hamiltonian for the Diatomic Chain in Terms of Normal Coordinates 

Substituting this expression in the kinetic energy in (2.3) gives 

According to (B.5), the sum over % is different from zero only if q = - q (here q and q are restricted to the first Brillouin zone). This result together with (2.48,31,25) leads to the expression 

The transformation of the potential energy in (2.3) is more complicated. Substitution of (2.47) in the sums 

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