International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 559-574

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

J. N. Boyd and P. N. Raychowdhury

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284, Virginia, USA

Received 21 November 1979

Copyright © 1980 J. N. Boyd and P. N. Raychowdhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.