$SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states

Abstract

We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the $su(1,1)$ Lie algebra. We construct the $SU(1,1)$ Perelomov radial coherent states for this problem and compute their time evolution.

arXiv comment14 pages

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Cited by in corpus (24)

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• Exact Solution of the Relativistic Dunkl Oscillator in $(2+1)$ Dimensions
• Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
• Dunkl-Graphene in constant magnetic field
• Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
• Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• Algebraic solution and coherent states for the Dirac oscillator interacting with a topological defect
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Dunkl-Schrodinger Equation in Higher Dimension
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• Time-dependent Dunkl-Pauli Oscillator
• Dunkl-Klein-Gordon Equation in Higher Dimensions
• 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
• Exact Solutions of the Schrödinger-Dunkl Equation for a Free Particle in a Finite and Infinite Cylindrical Well
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties