A method for asymptotic integration of almost diagonal systems

Abstract

A theorem of asymptotic integration is proven for linear systems of differential equations. The theorem is designed to fit a specialized family of differential systems which occur frequently in quantum mechanics. It is shown to be best possible in a certain sense. The method provided differs from an established trend that transforms the differential system, via a preparation theorem, to a differential system, where the coefficient matrix is the sum of a diagonal matrix and a remainder matrix that must be absolutely integrable at infinity. In this work the fundamental matrix solution is given as a product of a diagonal matrix and a perturbation of the identity matrix. The perturbation of the identity matrix being on the right in the product rather than on the left as is common in the literature.