Spectral properties of non-conservative multichannel SUSY partners of the zero potential

Abstract

Spectral properties of a coupled $N\times N$ potential model obtained with the help of a single non-conservative supersymmetric (SUSY) transformation starting from a system of $N$ radial Schrödinger equations with the zero potential and finite threshold differences between the channels are studied. The structure of the system of polynomial equations which determine the zeros of the Jost-matrix determinant is analyzed. In particular, we show that the Jost-matrix determinant has $N{2}^{N-1}$ zeros which may all correspond to virtual states. The number of bound states satisfies $0\le n_b\le N$. The maximal number of resonances is $n_r=(N-1)2^{N-2}$. A perturbation technique for a small coupling approximation is developed. A detailed study of the inverse spectral problem is given for the $2\times 2$ case.

17 pages, 4 figures

References in corpus (2)

• Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics
• Supersymmetric transformations for coupled channels with threshold differences

Cited by in corpus (1)

• Coupling between scattering channels with SUSY transformations for equal thresholds