
Accession Number : AD0737247
Title : The Scattering Matrix Associated with NonSelfadjoint 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 Smatrix for the Schroedinger operator, A = delta + q(x), with a complexvalued potential a(x). Since A is not selfadjoint, the scattering process is not energy conserving. However, it will be shown that almost all of the basic properties of the Smatrix carry over from the selfadjoint case. This includes the meromorphic continuation of the Smatrix 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 Smatrix (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