Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential

Abstract

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate solutions for two important problems in three-dimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the Dunkl-Klein-Gordon oscillator solutions with the Cartesian and spherical coordinates. In both coordinate systems, we find that the differential equations are separable and their eigenfunctions can be given in terms of the associate Laguerre and Jacobi polynomials. We observe how the Dunkl formalism is affecting the eigenvalues as well as the eigenfunctions. As a second problem, we examine the Dunkl-Klein-Gordon equation with the Coulomb potential. We obtain the eigenvalue, their corresponding eigenfunctions, and the Dunkl-fine structure terms.

8 pages, 1 fig

References in corpus (5)

• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation
• Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
• The Bannai-Ito algebra and some applications
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• Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
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• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
• Dunkl-Schrodinger Equation in Higher Dimension
• 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
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• On Dunkl-Bose-Einstein Condensation in Harmonic Traps
• 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
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties