Abstract
This chapter discusses the elementary aspects of the band theory of solids. The translational symmetry of the crystal is considered in the chapter assuming there are no point group operations, that is, a triclinic crystal. This leads to the concept of the wave vector of the crystal k being a label of an irreducible representation. When cyclic boundary conditions are imposed on the crystal, one is lead to the concept of a finite number of k values that can be restricted to a zone in k-space, reciprocal lattice space. This brings in, via reciprocal space, the concept of the Brillouin zones and reciprocal lattice vectors. Bloch functions are the basis functions of the irreducible representations of the translational group. The bands can be made up of 1s-, 2s-, 2p-like wave functions with the phase modulated over the unit cells as the k values are varied. These considerations apply to symmorphic as well as nonsymmorphic space groups.
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