A New Picture of the Vibration of Linear Lattices

A new version of the method of transfer matrix is presented, which largely simplifies the derivation of eigenfrequency equation, on the one hand, and gives rise to a very simple and vivid picture (vector picture), on the other hand, of the normal vibration for the linear isotopic lattices. By using this version and the vector picture, the wave forms of the extra- and in-band vibrations of the lattices containing a small amount of impurity and the eigenfrequency spectrum of generalized diatomic lattices are discussed, obtaining some interesting conclusions.