Exact solution of the relativistic Dunkl oscillator in (2+1) dimensions

Journal Article · Sun Dec 15 04:00:00 EST 2019 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2019.167964· OSTI ID:22852353

Mota, R. D. ^[1]; Salazar-Ramírez, M. ^[2]; Granados, V. D. ^[3]

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1. 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)
2. 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)
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)

In this paper we study the (2+1)-dimensional Dirac–Dunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial derivatives by the Dunkl derivatives. We solve the Dunkl–Klein–Gordon-type equations in polar coordinates in a closed form. The angular part eigenfunctions are given in terms of the Jacobi–Dunkl polynomials and the radial functions in terms of the Laguerre functions. Also, we compute the energy spectrum of this problem and show that, in the non-relativistic limit, it properly reduces to the Hamiltonian of the two dimensional harmonic oscillator.

• OSTI ID: 22852353
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 411; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC EQUATION
EIGENFUNCTIONS
ENERGY SPECTRA
EXACT SOLUTIONS
HAMILTONIANS
HARMONIC OSCILLATORS
KLEIN-GORDON EQUATION
MAGNETIC FIELDS
POLYNOMIALS
RELATIVISTIC RANGE
TWO-DIMENSIONAL SYSTEMS