论文标题
部分可观测时空混沌系统的无模型预测
Energy spectrum design and potential function engineering
论文作者
论文摘要
Starting with an orthogonal polynomial sequence $\{p_n(s)\}_{n=0}^\infty$ that has a discrete spectrum, we design an energy spectrum formula, $E_k = f (s_k)$, where $|{s_k\}$ is the finite or infinite discrete spectrum of the polynomial.使用最新的方法来进行量子力学，而不是基于潜在功能，而是基于正交能量多项式，我们对与所选能量谱相关的潜在函数进行了局部数值实现。在这项工作中，我们选择三参数连续双Hahn多项式为例。给出了相应结合状态能谱，散射状态相移和波形的确切分析表达式。但是，仅针对给定的一组物理参数获得电位函数。
Starting with an orthogonal polynomial sequence $\{p_n(s)\}_{n=0}^\infty$ that has a discrete spectrum, we design an energy spectrum formula, $E_k = f (s_k)$, where $|{s_k\}$ is the finite or infinite discrete spectrum of the polynomial. Using a recent approach for doing quantum mechanics based, not on potential functions but, on orthogonal energy polynomials, we give a local numerical realization of the potential function associated with the chosen energy spectrum. In this work, we select the three-parameter continuous dual Hahn polynomial as an example. Exact analytic expressions are given for the corresponding bound states energy spectrum, scattering states phase shift, and wavefunctions. However, the potential function is obtained only numerically for a given set of physical parameters.
