Symmetry characterization of electrons and lattice excitations

Abstract

Abstract. Symmetry concerns all aspects of a physical system from the electronic orbitals to structural and magnetic excitations. In this article we will try to elaborate the fundamental connection between symmetry and excitations. As excitations are manyfold in physical systems it is impossible to treat them exhaustively. We thus concentrate on the two topics of Bloch electrons and phonons. These two examples are complementary in the sense that Bloch electrons describe single particles in an external periodic potential while phonons exemplify a decoupled system of interacting particles. The way we develop the argument gives as by-product a short account of molecular orbitals and molecular vibrations.

An introduction to the theory of nuclear neutron scattering in condensed matter

“…where V j ( r − R j ) is the interaction potential of an individual scatterer characterised by its position operator R j . 54 The second equality underlines the fact that we are dealing with a convolution of the positions with the interaction potentials. The first step in the evaluation of the master equation consists in the integration over the variable r of the matrix element λ f , k f |V |λ i , k i , which is at the heart of the master equation.…”

“…We are not going to pursue the discussion of these selection rules that can be derived using group theory. The interested reader can consult the literature [19,45,54].…”