Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
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精确可解的量子力学和多索引正交多项式的无限族
DOI：
10.1016/j.physletb.2011.06.075
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发表时间：
2011
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.Matsuzaki;K.Yamawaki;江尻信司;片岡啓介;S. Odake and R. Sasaki
发现了无限多指标正交多项式族作为精确可解的一维量子力学系统的解。最简单的例子，单指标正交多项式，是由本文作者构造的I型和II型的例外拉盖尔和雅可比多项式的无限族。新多项式的整数指标的总和是有限的，它们对应于通过推广Crum-Adler定理而被“删除”的“虚态波函数”的度。每个多项式都有另一个整数n来计算节点。
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of types I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the ‘virtual state wavefunctions’ which are ‘deleted’ by the generalisation of Crum–Adler theorem. Each polynomial has another integer n which counts the nodes.