基于Horváth和Apagyi最近提出的辅助逆Sturm-Liouville问题的逆散射方法[Mod. B 22，2137（2008）]的方法进行了多方面的研究，并进一步发展，以（重新）构建三维薛定谔方程中实现的紧支撑的球对称固定能势。该方法被推广到获得一个家庭的逆程序，其特征在于由两个参数起源，分别从刘维尔变换和逆Sturm-Liouville问题的解决方案。这两个参数的影响所产生的辅助逆谱问题的束缚态，其中之一，使他们的数量减少，这是由一个简单的方法进行评估。提出了基本矩问题的各种求解方法，包括精确的柯西矩阵求逆法、伪束缚态的使用和束缚态数目的估计。实例包括从理论上已知的或从散射实验导出的相移产生电势。
英文摘要：
An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horváth and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct spherically symmetric fixed energy potentials of compact support realized in the three-dimensional Schrödinger equation. The method is generalized to obtain a family of inverse procedures characterized by two parameters originating, respectively, from the Liouville transformation and the solution of the inverse Sturm-Liouville problem. Both parameters affect the bound states arising in the auxiliary inverse spectral problem and one of them enables to reduce their number which is assessed by a simple method. Various solution techniques of the underlying moment problem are proposed including exact Cauchy matrix inversion method, usage of spurious bound state and assessment of the number of bound states. Examples include (re)productions of potentials from phase shifts known theoretically or derived from scattering experiments.
