Multichannel framework for singular quantum mechanics

• A multichannel framework is proposed for singular quantum mechanics and analogues.
• The framework unifies several established approaches for singular potentials.
• Singular points are treated as new scattering channels.
• Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix.
• Conformal quantum mechanics and the inverse quartic potential are highlighted.

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.