Collective-Variable Description of the Dynamics of Crystals.

Abstract

A description is given of the dynamics of crystals by meaus of co]lective variables, namely the Fourier transforms of the divergence and curl of the current. It is shown that, in the harmonio approximation, the classical equations of motion are reduced to a set of three equations involving only the collectiye variables themselves. From these equations the usual result for the frequency of phonons is obtained. Further-more. the quantum-mechanical equations of motion can again be reduced in a suitable approximation, to a set of three coupled equations in the collective variables. A relationship between frequency and wave number is derived for the excitations of the system from them.