The singular and the 2:1 anisotropic Dunkl oscillators in the plane

@article{Genest2013TheSA,
  title={The singular and the 2:1 anisotropic Dunkl oscillators in the plane},
  author={Vincent X. Genest and Luc Vinet and Alexei S. Zhedanov},
  journal={arXiv: Mathematical Physics},
  year={2013}
}
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl oscillator is second-order superintegrable and admits separation of variables in both Cartesian and polar coordinates. The spectrum of the Hamiltonian is obtained algebraically and the separated wavefunctions are given in the terms of Jacobi, Laguerre and… 
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