Eur. Phys. J. Plus (2017) 132: 39
https://doi.org/10.1140/epjp/i2017-11314-3

Regular Article

SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states

¹ Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Del. Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico
² Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Del. Coyoacán, C.P. 04430, Ciudad de México, Mexico
³ Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Del. Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

^* e-mail: escomphysics@gmail.com.mx

Received: 11 November 2016
Accepted: 20 December 2016
Published online: 24 January 2017

Abstract

We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.