A method for asymptotic integration of almost diagonal systems

Article type: Research Article

Authors: Elias, Uri | Gingold, Harry

Affiliations: Department of Mathematics, Technion – I.I.T., Haifa 32000, Israel E‐mail: elias@tx.technion.ac.il | Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA E‐mail: gingold@math.wvu.edu

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.

Journal: Asymptotic Analysis, vol. 29, no. 3-4, pp. 343-357, 2002