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

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, ∆xmin=ℏ3β+β′, where β and β′ 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 β≠0. Not only in the nonrelativistic limit but also in the limit of the standard case (β=β′=0), our results reduce to well known usual ones