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arXiv · 1206.0480

Families of superintegrable Hamiltonians constructed from exceptional polynomials

Sarah Post·Satoshi Tsujimoto·Luc Vinet
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Abstract

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.

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Sarah Post, Satoshi Tsujimoto, Luc Vinet. 2012-06-03. Families of superintegrable Hamiltonians constructed from exceptional polynomials. https://doi.org/10.1088/1751-8113/45/40/405202

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