Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

For the conventional translational shape-invariant potentials (TSIPs), it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.     

利用改进的同伦算法求解特征值问题

矩阵特征值问题是机器学习、数据处理以及工程分析和计算中经常需要解决的问题之一.同伦算法是求解矩阵特征值的经典方法;自动微分可以有效、快速地计算出大规模问题相关函数的导数项,并且可以达到机器精度.充分利用自动微分的优点,设计自动微分技术与同伦算法相结合的方法求解矩阵特征值问题.数值实验验证了该算法的有效性.     

Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

For the conventional translational shape-invariant potentials (TSIPs), it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.