Abstract. Pairs of SUSY partner Hamiltonians are studied which are interrelated by usual (linear) or polynomial supersymmetry. Assuming the model of one of the Hamiltonians as exactly solvable with known propagator, expressions for propagators of partner models are derived. The corresponding general results are applied to "a particle in a box", the Harmonic oscillator and a free particle (i.e. to transparent potentials).

A second-order supersymmetric transformation is presented, for the two-channel Schrödinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Padé expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton 3 S1-3 D1 case.PACS numbers: 03.65. Nk, 03.65.Ge, 13.75.Cs In quantum scattering theory, the fundamental inverse problem consists in deducing the interaction potential between two colliding particles from their experimental elastic-scattering cross sections [1]. These cross sections have first to be parametrized in terms of energy-dependent partial-wave phase shifts or scattering matrices. For a central interaction V (r), the partial waves decouple and a sequence of single-channel inverse problems have to be solved. For more complicated interactions, like the tensor interaction in nuclear physics, partial waves may be coupled and matrix potentials have to be constructed from coupled-channel scattering matrices.A formal solution to these inverse problems can be written in terms of integral equations [1]. In practical applications, experimental data turn out to be precisely parametrizable in terms of separable kernels for these equations. These correspond to scattering matrices that are rational functions of the wave number. The integral equations can then be solved analytically and the corresponding potentials are also expressed in a separable form. This procedure applies to both the singleand coupled-channel cases [2,3]. In the single-channel case, the same potentials can be constructed with the help of supersymmetric quantum mechanics (SUSYQM) [4,5]. This method is much simpler than the integral-equation one, as the potential is directly related to its scattering-matrix poles. Moreover, a small number of poles is in general sufficient to fit experimental data on the whole elastic-scattering energy range; this is in particular the case for the neutron-proton singlet (spin 0) channels [6,7], that decouple because of the vanishing tensor interaction.The present Letter aims at extending this very efficient single-channel method to the two-channel case without threshold difference, and at applying it to the neutron-proton triplet (spin 1) coupled channels. This system was studied in the framework of the integral-equation method by Newton and Fulton [2], at low energy, and by Kohlhoff and von Geramb [3], on the whole elastic-scattering range. The present paper subsumes these works, by separating the effect of the coupling between channels in the inversion procedure, by parametrizing the data with a minimal number of poles, and by deriving simple expressions for the corresponding matrix potential.We consider two channels with equal thresholds and angular momenta l and l + 2. The scatter...

Starting from a system of N radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled N × N exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on N (N + 1)/2 unconstrained parameters and on one upperbounded parameter, the factorization energy. A detailed study of the model is done for the 2×2 case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable 2 × 2 atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.

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 phaseequivalent transformations, the mixing parameter is modified by the eigenphase preserving transformation.