Algebraic approach for the one-dimensional Dirac-Dunkl oscillator

Abstract

We extend the $(1+1)$-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate $su(1,1)$ algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the $su(1,1)$ irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

16 pages

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• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• 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
• The Generalized Fokker-Planck Equation in terms of Dunkl-type Derivatives
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature
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• Dunkl-Schrodinger Equation in Higher Dimension
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
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• 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
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties
• Exact Solutions of the Schrödinger-Dunkl Equation for a Free Particle in a Finite and Infinite Cylindrical Well