线上多道逆散射问题：束缚态和束缚态
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
摘要：
考虑了有限支撑势下存在阈值和束缚态的一维多通道逆散射问题。利用莱文表示，我们推导出一般的Marchenko积分方程的N-耦合通道，并表明，与径向逆散射问题的情况下，结合态能量和渐近归一化常数的信息可以推断，从反射系数矩阵单独。因此，给定该矩阵，Marchenko逆散射过程可以为我们提供唯一的多通道势。讨论了它与超对称伙伴势的关系以及可能的应用。积分方程已实施数值和应用到几个示意性的例子显示多通道系统的特性。一个可能的应用程序的形式主义的技术问题进行了简要的讨论。
英文摘要：
We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
