Analytic Structure of the S-Matrix for Singular Quantum Mechanics

TL;DR

This paper analyzes the analytic structure of the S-matrix in singular quantum mechanics, focusing on how boundary conditions and physical properties influence its behavior, including unitarity and time-reversal invariance.

Contribution

It provides a mathematical and physical characterization of the S-matrix's analytic structure in singular quantum mechanics, linking nonunitary solutions to unitary families.

Findings

Characterization of S-matrix behavior via unitarity and Wronskian relations

Interpretation of nonunitary solutions through unitary families

Application of Blaschke factorization to the S-matrix

Abstract

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter ($\Omega$) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.