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Advances in High Energy Physics
Volume 2013, Article ID 383957, 10 pages
Research Article

Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy

1Laboratoire de Physique Mathématique et Subatomique (lpmps), Départment de Physique, Faculté des Sciences Exactes, Université Constantine1, 25000 Constantine, Algeria
2Laboratoire de Physique Quantique et Systémes Dynamiques, Département de Physique, Faculté des Sciences, Université Ferhat Abbas Sétif 1, 19000 Setif, Algeria
3Department of Radiologic Technology, Daegu Health College, Yeongsong-ro 15, Daegu 702-722, Republic of Korea

Received 3 July 2013; Accepted 17 August 2013

Academic Editor: Gongnan Xie

Copyright © 2013 Malika Betrouche et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length with the order of the Planck length, , where β and are two positive small parameters. Wave functions of the system and the corresponding energy spectrum are derived rigorously. The presence of the minimal length accompanies a quadratic dependence of the energy spectrum on quantum number n, implying the property of hard confinement of the system. It is shown that the infinite degeneracy of energy levels appearing in the usual Dirac oscillator is vanished by the presence of the minimal length so long as . Not only in the nonrelativistic limit but also in the limit of the standard case , our results reduce to well known usual ones.