Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space

Abstract

In this paper, we examine the harmonic oscillator problem in non-commutative phase space (NCPS) by using the Dunkl derivative instead of the habitual one. After defining the Hamilton operator, we use the polar coordinates to derive the binding energy eigenvalue. We find eigenfunctions that correspond to these eigenvalues in terms of the Laguerre functions. We observe that the Dunkl-Harmonic Oscillator (DHO) in the NCPS differs from the ordinary one in the context of providing additional information on the even and odd parities. Therefore, we conclude that working with the Dunkl operator could be more appropriate because of its rich content.

11 pages 4 Figures

References in corpus (10)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
• $SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states
• Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Thermal Properties of Relativistic Dunkl Oscillators
• Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator
• Pauli Oscillator In Noncommutative Space
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D

Cited by in corpus (12)

• 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
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• Dunkl-Klein-Gordon Equation in Higher Dimensions
• 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