Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1857405 | Annals of Physics | 2014 | 26 Pages |
•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.