Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations
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DOI：
10.1088/1751-8113/43/31/315204
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
R. Sasaki;S. Tsujimoto;A. Zhedanov
中科院分区：
文献类型：
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作者：
R. Sasaki;S. Tsujimoto;A. Zhedanov
给出了对应于例外的拉盖尔多项式和雅可比多项式的无限多形状不变哈密顿量的四个族的简单推导。 Darboux-Crum 变换用于将众所周知的径向振子形状不变哈密顿量和 Darboux-Pöschl-Teller 势与 Odake-Sasaki 形状不变势联系起来。杜塔和罗伊用这种方法推导出了特殊拉盖尔多项式的两个最低成员。该方法被扩展至其完全的通用性，并讨论了许多其他分支，包括广义博赫纳问题的各个方面和特殊正交多项式的双谱性质。
A simple derivation is presented of the four families of infinitely many shape-invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. The Darboux–Crum transformations are applied to connect the well-known shape-invariant Hamiltonians of the radial oscillator and the Darboux–Pöschl–Teller potential to the shape-invariant potentials of Odake–Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of the generalized Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.