Saxon-Hutner-Luttinger theorem in various physical models in one dimension.

Abstract

The Saxon-Hutner-Luttinger theorem is proved herein by using a very simple mathematical scheme within the transfer-matrix method for one-dimensional Schr\"odinger operators in various types of physical models. This theorem is extended to that for the regular and the disordered chain systems, where binary types of regularity and disorder are assumed throughout the paper. This scheme is very general and does not depend upon the explicit forms of transfer matrices in the models. Clarified is the relationship between Anderson localization and the Saxon-Hutner-Luttinger theorem.