Eigenphase preserving two-channel SUSY transformations

Abstract

We propose a new kind of supersymmetric (SUSY) transformation in the case of the two-channel scattering problem with equal thresholds, for partial waves of the same parity. This two-fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions. We call it an eigenphase preserving SUSY transformation as it relates two Hamiltonians, the scattering matrices of which have identical eigenphase shifts. In contrast to known phase-equivalent transformations, the mixing parameter is modified by the eigenphase preserving transformation.

16 pages, 1 figure

References in corpus (8)

• Chains of Darboux transformations for the matrix Schroedinger equation
• Phase equivalent chains of Darboux transformations in scattering theory
• Phase shift effective range expansion from supersymmetric quantum mechanics
• Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance
• Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics
• Supersymmetric transformations for coupled channels with threshold differences
• Coupling between scattering channels with SUSY transformations for equal thresholds
• Spectral properties of non-conservative multichannel SUSY partners of the zero potential

Cited by in corpus (5)

• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Generic matrix superpotentials
• Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method
• Singular matrix Darboux transformations in the inverse scattering method
• Multichannel generalization of eigen-phase preserving supersymmetric transformations