Andrey M Pupasov et al 2008 J. Phys. A: Math. Theor. 41 175209 doi:10.1088/1751-8113/41/17/175209
Spectral properties of non-conservative multichannel SUSY partners of the zero potential
Andrey M Pupasov1,2, Boris F Samsonov1 and Jean-Marc Sparenberg2
Show affiliationsSpectral properties of a coupled N × 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 N2N−1 zeros which may all correspond to virtual states. The number of bound states satisfies 0 ≤ nb ≤ N. The maximal number of resonances is nr = (N − 1)2N−2. A perturbation technique for a small coupling approximation is developed. A detailed study of the inverse spectral problem is given for the 2 × 2 case.
- PACS
- MSC
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81U40 Inverse scattering problems
15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)
81Q60 Supersymmetric quantum mechanics
81Q15 Perturbation theories for operators and differential equations
- Subjects
- Dates
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Issue 17 (2 May 2008)
Received 9 January 2008, in final form 25 February 2008
Published 15 April 2008
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Spectral properties of non-conservative multichannel SUSY partners of the zero potential
Andrey M Pupasov et al 2008 J. Phys. A: Math. Theor. 41 175209
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