A chain consists of alternating atoms of types A and B. There are N atoms of each type. Each atom has one electron in an s-orbital. The separation between adjacent atoms is a/2, so that the lattice constant is a. Assume periodic boundary conditions. Assume further that the orbitals on different atoms are orthogonal and that interactions exist only between nearest neighbors, and that the matrix element of the Hamiltonian between orbitals on adjacent atoms is -t (these are the same assumptions we made in the tight binding model in graphene). Requied:
Calculate and plot the energy E as a function of k in the first Brillouin zone.