Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators

Abstract

Dunkl derivative enriches solutions by discussing parity due to its reflection operator. Very recently, one of the authors of this manuscript presented one of the most general forms of Dunkl derivative that depends on three Wigner parameters to have a better tuning. In this manuscript, we employ the latter generalized Dunkl derivative in a relativistic equation to examine two-dimensional harmonic and anharmonic oscillators solutions. We obtain the solutions by Nikiforov-Uvarov and QES methods, respectively. We show that degenerate states can occur according to the Wigner parameter values.

arXiv comment12 pages, 4 figures

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Cited by in corpus (16)

• On the Path Integral Formulation of Wigner-Dunkl Quantum Mechanics
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• 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
• The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Dunkl-Schrodinger Equation in Higher Dimension
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• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• 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
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties