The Scattering Matrix Associated with Non-Selfadjoint Differential Operators.
Abstract
The purpose of the paper is to study the S-matrix for the Schroedinger operator, A = -delta + q(x), with a complex-valued potential a(x). Since A is not self-adjoint, the scattering process is not energy conserving. However, it will be shown that almost all of the basic properties of the S-matrix carry over from the self-adjoint case. This includes the meromorphic continuation of the S-matrix and the connection between its poles and resonant states. It is also shown that when q(x, epsilon) depends analytically on a complex parameter epsilon, the S-matrix (and its poles) depend analytically (fractionally analytically) on epsilon. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0737247
Entities
People
- Charles Goldstein
Organizations
- University of Wisconsin–Madison