Eur. Phys. J. Plus (2018) 133: 161
https://doi.org/10.1140/epjp/i2018-11986-y

Regular Article

-deformed Dirac oscillator in an external magnetic field

¹ Physics Department, College of Science and Arts at Ar Rass, Qassim University, PO Box 53, 51921, Ar Rass, Saudi Arabia
² Université de Tunis El Manar, Faculté des Sciences de Tunis, Unité de Recherche de Physique Nucléaire et des Hautes Energies, 2092, Tunis, Tunisia
³ Department of Mathematics, College of Science and Arts at Ar Rass, Qassim University, PO Box 53, 51921, Ar Rass, Saudi Arabia
⁴ Université de Sfax, Institut Préparatoire aux Études d’Ingénieurs de Sfax, 3072, Sfax, Tunisia

^* e-mail: yassine.chargui@gmail.com

Received: 14 January 2018
Accepted: 21 March 2018
Published online: 24 April 2018

Abstract

We study the solutions of the (2 + 1)-dimensional -deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the -deformation.