2021/07/30 by R. D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez +2 · 3 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Nonlinear Waves and Solitons #Nonlinear Photonic Systems
paper · doi:10.1142/s0217732321501716
We introduce the Dunkl–Klein–Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein–Gordon (KG) equation. We show that the generalization with Dunkl derivative of the z-component of the angular momentum is what allows the separation of variables of the DKG equation. Then, we compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential and the Klein–Gordon oscillator analytically and from an su(1, 1) algebraic point of view. Finally, we show that if the parameters of the Dunkl derivative vanish, the obtained results suitably reduce to those reported in the literature for these 2D problems.