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.