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# ex02 - Solid State Theory Exercise 2 Point groups and their...

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Solid State Theory Exercise 2 FS 11 Prof. M. Sigrist Point groups and their representations Exercise 2.1 Energy bands of almost free electrons on the fcc lattice Let us consider almost free electrons on a face-centered cubic (fcc) lattice. The goal of this exercise is to compute the lowest energy bands along the Δ-line using degenerate perturbation theory and the machinery of group theory . Remember that in reciprocal space, the fcc lattice transforms into a body-centered cubic (bcc) lattice. The point group of the cubic Bravais lattices (simple cubic, fcc, bcc) is denoted by O h (symmetry group of a cube). Its character table is given in Tab. 1. a) We first study the Γ point ( ~ k = 0). For free electrons ( V = 0) the lowest energy level is non-degenerate and the second one has an eight fold degeneracy. We focus on the second level and denote the eight-dimensional representation of O h defined on this subspace by Γ. Find the irreducible representations contained in Γ. Compute the group character χ Γ

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ex02 - Solid State Theory Exercise 2 Point groups and their...

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