Group Theory in Solid State Physics

Abstract

This chapter discusses stationary states in the quantum theory of matter, group of the Hamiltonian, symmetry groups of solids, lattice vibrations in solids, and band theory of solids. Group theory has become a most useful tool in modern physics for systematizing the description of idealized processes dealing with theoretical concepts such as energy, mass, charge, momentum, and angular momentum; for classifying states in the quantum theory of matter; and further, for simplifying numerical applications of physical laws. The symmetry of a physical system is because of idealizations, such as closed systems, isotropic spaces, ideal gases, incompressible fluids, and perfect solids. Crystal symmetry is an interesting subject for detailed study because of the variety of lattice structures occurring in nature. Considerations of symmetry alone may be the most essential part of the work in determining the properties of crystalline solids. It is necessary to make use of the crystal symmetry in order to be able to obtain numerical solutions for the equations of motion of identical particles, such as electrons, phonons, or photons, moving in perfect solids.