Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation

Abstract

We introduce a generalization of the Dunkl-derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.

12 pages

References in corpus (11)

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Cited by in corpus (10)

• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• 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
• 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