标题： 零势能非保守多通道 SUSY 伙伴的谱性质 显示英文标题

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

摘要： 耦合$N \times N$势模型的谱性质通过从具有零势和通道间有限阈值差的$N$径向薛定谔方程出发，借助单个非保守超对称(SUSY)变换获得，这些性质被研究了。 确定Jost矩阵行列式零点的多项式方程组的结构被分析。 特别是，我们表明 Jost矩阵行列式有$N2^{N-1}$个零点，这些零点可能都对应于虚态。 束缚态的数量满足$0\leq n_b\leq N$。 最大共振数是$n_r=(N-1)2^{N-2}$。 发展了一种用于小耦合近似的微扰技术。 给出了$2\times 2$情况下的逆谱问题的详细研究。 显示英文摘要

摘要： 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.