On the spectrum of the normal frequencies of a polar crystal lattice

Abstract

In a previous joint paper with M. Born the importance of the lattice frequency spectrum in problems concerning the physical properties of the solid state was discussed; and a possible method for its determination was suggested and briefly outlined. This pervious note provides a suitable introduction to the present paper, as the method, suggested there, is here used to build up the general theory required for the numerical determination of the lattice frequency spectrum. The development of the general theory is most easily understood after an examination of the problem in the case of the one-dimensional crystal model. There, on account of the simplicity of the model, all the mathematical difficulties of the general theory are avoided, and the significance of each step is always apparent.