Exact solutions of the generalized Dunkl oscillator in the Cartesian system

• Published in: Annals of physics Vol. 451; p. 169259
• Main Authors: Dong, Shi-Hai, Quezada, L.F., Chung, W.S., Sedaghatnia, P., Hassanabadi, H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-04-2023
• Subjects: Dunkl derivatives; Dunkl Schrödinger equation; Exact solutions; Exact solutions; Dunkl derivatives; Dunkl Schrödinger equation
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2023.169259

In this paper, we use the generalized Dunkl derivatives instead of the standard partial derivatives in the Schrödinger equation to obtain an explicit expression of the generalized Dunkl–Schrödinger equation in 3D. It was found that this generalized Dunkl–Schrödinger equation for the 3D harmonic oscillator is exactly solvable in the Cartesian coordinates. From the relevant commutation relations, it is evident that the symmetry possessed by the original Dunkl Harmonic oscillator is broken by the generalized Dunkl derivative. Finally, we show that energy levels can be affected by considering a deformation parameter ɛ.
•Generalized Dunkl derivative is studied.•3D harmonic oscillator in Cartesian coordinates is investigated.•The condition of the sd(3) algebra are studied.•The effect of deformation parameter in the energy of harmonic oscillator is studied.