Families of superintegrable Hamiltonians constructed from exceptional polynomials
Families of superintegrable Hamiltonians constructed from exceptional polynomials
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DOI：
10.1088/1751-8113/45/40/405202
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
S. Post;S. Tsujimoto;L. Vinet
中科院分区：
文献类型：
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作者：
S. Post;S. Tsujimoto;L. Vinet
我们引入了一族精确可解的二维哈密顿量，它们的波函数是用拉盖尔多项式和例外雅可比多项式给出的。哈密顿包含纯量子项，这些项在经典极限中消失，只剩下一族已知的超可积系统。此外，对于所考虑的正交多项式，由梯形算子构造了运动的高阶积分，证明了量子系统是超可积的。
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable.