论文标题
一种用于解决逆量子散射问题的传输操作员方法
A transmutation operator method for solving the inverse quantum scattering problem
论文作者
论文摘要
考虑了扰动贝塞尔方程的逆量子散射问题。提出了一种解决问题的直接和实用方法。它允许人们将反问题减少到线性代数方程系统，并从系统的解决方案向量的第一个组件中回收电势。该方法基于trans变运算符内核和Gelfand-Levitan方程的特殊形式的傅里叶 - 雅各比级序列表示，该方程用于获得线性代数方程系统。证明了该方法的收敛性和稳定性，以及截短系统解的存在和独特性。讨论了该方法的数值实现。提供了数值测试的结果，揭示了该方法的明显准确性和稳定性。
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic equations, and the potential is recovered from the first component of the solution vector of the system. The approach is based on a special form Fourier-Jacobi series representation for the transmutation operator kernel and the Gelfand-Levitan equation which serves for obtaining the system of linear algebraic equations. The convergence and stability of the method are proved as well as the existence and uniqueness of the solution of the truncated system. Numerical realization of the method is discussed. Results of numerical tests are provided revealing a remarkable accuracy and stability of the method.
