超对称展开算法及Hulthén势与非简谐势的完整解析解
Supersymmetric Expansion Algorithm and complete analytical solution for the Hulthén and anharmonic potentials
AI总结：
本文提出超对称展开算法，将对数展开法与超对称量子力学结合，通过无节点边缘态逐阶求解，首次获得三维Hulthén势和一维非简谐振荡子势的完整解析解。
摘要：
本文阐述了一种为非精确可解势的薛定谔方程提供解析解的算法。该算法代表了对数展开法与超对称量子力学技术的结合，并将后者扩展至非形状不变势。给定哈密顿量$H_{0}$的完整解由哈密顿量$H_{0}$及其一组超对称伙伴$H_{1}, H_{2},..., H_{r}$的无节点态获得。这些无节点态（称为“边缘”态）是唯一的，通常可以是基态或激发态。它们通过对数展开法求解，该方法产生无穷多个耦合的一阶层级微分方程系统，随后转化为具有递推关系的代数方程，可逐阶求解。我们逐步阐述了上述方案，称之为“超对称展开算法”，并首次将其应用于获得三维Hulthén势和一维非简谐振荡子势的完整解析解。
英文摘要：
An algorithm for providing analytical solutions to Schrödinger's equation with non-exactly solvable potentials is elaborated. It represents a symbiosis between the logarithmic expansion method and the techniques of the superymmetric quantum mechanics as extended toward non shape invariant potentials. The complete solution to a given Hamiltonian $H_{0}$ is obtained from the nodeless states of the Hamiltonian $H_{0}$ and of a set of supersymmetric partners $H_{1}, H_{2},..., H_{r}$. The nodeless states (dubbed "edge" states) are unique and in general can be ground or excited states. They are solved using the logarithmic expansion which yields an infinite systems of coupled first order hierarchical differential equations, converted later into algebraic equations with recurrence relations which can be solved order by order. We formulate the aforementioned scheme, termed to as "Supersymmetric Expansion Algorithm'' step by step and apply it to obtain for the first time the complete analytical solutions of the three dimensional Hulthén--, and the one-dimensional anharmonic oscillator potentials.
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。
