Dirac oscillator with nonzero minimal uncertainty in position
By Christiane Quesne, V. Tkachuk. 2004
165 citations recorded by the source corpus.
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 and cases, both features being connected with supersymmetry or, equivalently, the ? ? ?? 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 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.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2a1f858808da2c23665a15952e1a62d023a5d1de
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Generalized Uncertainty Principle: Approaches and Applications (2014, background): “• problem of 3-dimensional Dirac oscillator [79] and the solution of (1+1)-dimensional Dirac oscillator within Lorentz covariant algebra [80],”