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

Understand

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 generalized Hermite polynomials.