Vibrations of finite one dimensional chains

Abstract

It is shown that by introducing generating functions for the vibration amplitudes of atoms in a linear chain, one can reduce the determination of the normal modes and proper frequencies of the chain to a purely algebraic problem. The method is illustrated by applying it to the study of the vibrations of a finite diatomic linear chain of atoms interacting through nearest-neighbour Hooke's law forces. The results are discussed and compared with earlier work on the problem. The possibility of extension of the method to more general situations is indicated.