Multichannel Framework for Singular Quantum Mechanics

TL;DR

This paper introduces a multichannel S-matrix framework for singular quantum mechanics that unifies existing methods and clarifies boundary-condition ambiguities by incorporating additional channels at singularities, ensuring unitarity.

Contribution

It presents a novel multichannel approach that generalizes and unifies renormalization and self-adjoint extension methods in singular quantum mechanics.

Findings

Framework resolves boundary-condition ambiguities.

Ensures unitarity through a fully linked S-matrix.

Applicable to various scenarios including apparent nonunitary cases.

Abstract

A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant ("asymptotic") observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances.