Accession Number : AD0737247

Title :   The Scattering Matrix Associated with Non-Selfadjoint Differential Operators.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Goldstein,Charles

Report Date : DEC 1971

Pagination or Media Count : 38

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, COMPLEX VARIABLES), (*QUANTUM THEORY, *S MATRIX), ANALYTIC FUNCTIONS, MEROMORPHIC FUNCTIONS, PERTURBATION THEORY

Subject Categories : Numerical Mathematics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE