Difference schrödinger operators with linear and exponential discrete spectra
Difference schrödinger operators with linear and exponential discrete spectra
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具有线性和指数离散谱的差分薛定谔算子
DOI：
10.1007/bf00760860
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发表时间：
1993
影响因子：
1.2
通讯作者：
A. Zhedanov
中科院分区：
文献类型：
--
作者：
V. Spiridonov;L. Vinet;A. Zhedanov
使用因式分解方法，我们构造有限差分薛定谔算子（雅可比矩阵），其离散谱由独立的算术或几何级数组成。这样的系统源自相应达布变换链的周期性、orq-周期性闭包。 Charlier、Krawtchouk、Meixner 正交多项式、它们的 q 模拟以及其他一些经典多项式是 N = 1 和 N = 2（N 是闭合周期）的最简单示例。自然的概括涉及 Painlevé 超越的离散版本。
Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.