Band theory of solids: an introduction from the point of view of symmetry
The structure of much of solid-state theory comes directly from group theory, but until now there has been no elementary introduction to the band theory of solids using this approach. Employing the most basic of group theoretical ideas, and emphasizing the significance of symmetry in determining many of the essential concepts, this is the only book to provide such an introduction. Many topics were chosen with the needs of chemists in mind, and numerous problems are included to enable the reader to apply the major ideas and to complete some parts of the treatment. Physical scientists will also find this a valuable introduction to the field.
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atomic orbitals axis basis belong Bloch functions bond Bravais lattice Brillouin zone edge Brillouin zone face called cell functions centre coefficients configuration space conjugate consider coordinates corresponding crystal pattern cubic lattice cyclic group defined degeneracy degenerate denote direct product discussed eigenfunctions eigenvalue elements energy levels equal equation equivalent example face-centred cubic Fermi energy Fermi surface figure follows free-electron given group G group theory Hamiltonian identical integral invariant inversion irreducible representations labelled lattice constant linear chain linear combination matrix means metal momentum normal notation Notice obtained one-dimensional orthogonal pattern point periodic perturbation phonon plane waves point group position vector primitive cell Problem properties prove reciprocal lattice reciprocal vectors respectively result rotation second band shown in Fig silicon small representations space group subgroup symmetry operations Table tions transformation translation group translation vector translationally unit cell unit vectors values vanish Wannier functions wave function whereas