Analytic Structure of the S-Matrix for Singular Quantum Mechanics

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.