Physics – Quantum Physics
Scientific paper
2008-12-23
J. Phys. A: Math. Theor. 42, 195303, (19pp), 2009
Physics
Quantum Physics
Scientific paper
10.1088/1751-8113/42/19/195303
Supersymmetric (SUSY) transformations of the multi-channel Schr\"odinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are analyzed. Relations between Jost and scattering matrices of superpartner potentials are obtained. In particular, we show that a special type of SUSY transformation allows us to introduce a coupling between scattering channels starting from a potential with an uncoupled scattering matrix. The possibility for this coupling to be trivial is discussed. We show that the transformation introduces bound and virtual states with a definite degeneracy at the factorization energy. A detailed study of the potential and scattering matrices is given for the $2\times 2$ case. The possibility of inverting coupled-channel scattering data by such a SUSY transformation is demonstrated by several examples ($s-s$, $s-p$ and $s-d$ partial waves).
Baye Daniel
Pupasov Andrey M.
Samsonov Boris F.
Sparenberg Jean-Marc
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