The shifted eigenvalue problem and phonon frequencies

It is shown that there is a transformation between the phonon frequencies in certain similar crystals (eg Ge and ZnSe) if it is assumed that the force constants do not vary and only act between nearest neighbors; that is, the effect of varying the masses can be understood in a simple way. It is also shown how the partial densities of states associated with each mass can be projected out. Finally, using similar techniques, the eigenfrequencies of a simple version of the shell model in Ge are related to an equivalent rigid-ion model.