English

Families of superintegrable Hamiltonians constructed from exceptional polynomials

Mathematical Physics 2015-06-05 v2 math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.1206.0480,
  title  = {Families of superintegrable Hamiltonians constructed from exceptional polynomials},
  author = {Sarah Post and Satoshi Tsujimoto and Luc Vinet},
  journal= {arXiv preprint arXiv:1206.0480},
  year   = {2015}
}