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

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

2009-02-06

arxiv.org/abs/0902.1102v1

Journal Of Physics A: Mathematical and Theoretical, 41 (2008) 175209 (17pp)

Physics

Mathematical Physics

17 pages, 4 figures

Scientific paper

10.1088/1751-8113/41/17/175209

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 Schr\"odinger 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 $N2^{N-1}$ zeros which may all correspond to virtual states. The number of bound states satisfies $0\leq n_b\leq N$. 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.

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