Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
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多索引 Meixner 和 Little q-Jacobi (Laguerre) 多项式
DOI：
10.1088/1751-8121/aa6496
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S.Odake and R.Sasaki
中科院分区：
文献类型：
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作者：
S. Motonami;K. Mimura;M. Nakatake;Y. Shim;K. Wakita;H. Sato;Y. Utsumi;S. Ueda;K. Shimada;Y. Taguchi;H. Namatame;M. Taniguchi;G. Orudzhev;and N. Mamedov;S.Odake and R.Sasaki
作为多指数正交多项式项目的第四阶段，我们提出了在一维半无限晶格上定义的“离散量子力学”框架中的多指数Meixner 和小q-Jacobi (Laguerre) 多项式，并具有实数位移。它们以与先前报道的多索引拉盖尔和雅可比多项式类似的方式，通过多次应用达布变换的离散模拟或虚拟状态向量的 Crum-Krein-Adler 删除，从与原始正交多项式相对应的量子力学系统中获得。虚拟状态向量是矩阵薛定谔方程在所有具有负能量和无限范数的格点上的解。这与在有限格上定义的(q-)Racah系统形成鲜明对比，其中除了两个边界点之一之外，“虚拟状态”向量满足矩阵薛定谔方程。
As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of'discrete quantum mechanics' with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum–Krein–Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-) Racah systems defined on a finite lattice, in which the'virtual state'vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.