par Quesne, Christiane 
;Tkachuk, Volodymyr
Référence Journal of Physics A: Mathematical and General, 38, 8, page (1747-1765)
Publication Publié, 2005-02
;Tkachuk, VolodymyrRéférence Journal of Physics A: Mathematical and General, 38, 8, page (1747-1765)
Publication Publié, 2005-02
Article révisé par les pairs
| Résumé : | In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac oscillator. Supersymmetric quantum mechanical and shape-invariance methods are used to derive both the energy spectrum and wavefunctions in the momentum representation. As for the conventional Dirac oscillator, there are neither negative-energy states for E = -1, nor symmetry between the l = j - 1/2 and l = j + 1/2 cases, both features being connected with supersymmetry or, equivalently, the ω →-ω transformation. In contrast with the conventional case, however, the energy spectrum does not present any degeneracy pattern apart from that associated with the rotational symmetry. More unexpectedly, deformation leads to a difference in behaviour between the l = j - 1/2 states corresponding to small, intermediate and very large j values in the sense that only for the first ones supersymmetry remains unbroken, while for the second ones no bound state exists. © 2005 IOP Publishing Ltd. |
