Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum

Abstract

We generalise the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic algebra involving reflection operators and more generally $c_{\lambda }$ extended oscillator algebras with grading. We apply the construction on two-dimensional $c_{\lambda }$ oscillators. We also introduce two new superintegrable Hamiltonians that are the anisotropic Dunkl and the singular Dunkl oscillators. We construct the integrals and using this extended approach of the Daskaloyannis method with grading and we present an algebraic derivation of the energy spectrum of the two models from the finite dimensional unitary representations and show how their spectrum divides into different sectors and relates to the physical spectrum.

References in corpus (4)

• A Recurrence Relation Approach to Higher Order Quantum Superintegrability
• Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential
• On realizations of polynomial algebras with three generators via deformed oscillator algebras
• Imaginary Powers of the Dunkl Harmonic Oscillator

Cited by in corpus (5)

• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• Time-dependent Dunkl-Pauli Oscillator
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications