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**Dispersion relation and lattice constants**

I need to be able to calculate the period (which I believe is the lattice constant) for a 1D crystal given the energy wavevector relation. Is this possible?

I also have to find the Bravais lattice of a 2D crystal give a similar relation.

What is it that I have to calculate.

1D

E = u[n+(1/3)(-1)^n cos(kb)]

2D

E = u[n+(1/3)(-1)^n cos(kx b)Xcos(ky b)]

What I thought was that either b just is the lattice constant, or that you should impose the periodic boundry condition and calculate it that way, allthoigh all that did was cancel down to nothing so i'm not sure. Do I have to change to real space?

Also i've been able to plot it in MATLAB and allthough that shows a sort of lattice i'm not 100% sure that this is correct, and i'd like to be able to do it analytically.

Thanks

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