纠缠哈密顿算符的群论方法
Group theoretical approach to the intertwined Hamiltonians
摘要：
我们证明了薛定谔Hamilton量的有限差分Bäcklund公式是我们两人在前一篇论文中考虑的黎卡提方程组上变换群的一个特殊元素。然后，我们给出了一阶微分算子相关的哈密顿算子问题的群论解释。的推广的有限差分算法有关本征函数的{ \emph三}不同的哈密顿量被发现，并分析了一些说明性的例子的理论，找到新的潜力，其中一个本征函数和其相应的本征值是确切已知的。
英文摘要：
We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relating eigenfunctions of {\emph three} different Hamiltonians is found, and some illustrative examples of the theory are analyzed, finding new potentials for which one eigenfunction and its corresponding eigenvalue is exactly known.
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