Representation theory of finite abelian groups applied to a linear diatomic crystal

Abstract

After a brief review of matrix representations of finite abelian groups, projection operators are defined and used to compute symmetry coordinates for systems of coupled harmonic oscillators. The Lagrangian for such systems is discussed in the event that the displacements along the symmetry coordinates are complex. Lastly, the natural frequencies of a linear, diatomic crystal are determined through application of the Born cyclic condition and the determination of the symmetry coordinates.