κ-Deformation of an extended Dirac oscillator

Abstract

We study a deformation, based on the κ-Poincaré-Hopf algebra, of an extended version of the Dirac oscillator, where the latter is coupled to a pseudoscalar Coulomb potential. The energy eigenvalues and the corresponding eigenfunctions of the system are calculated to first order in the deformation parameter. We also show that the deformation brings the usual intrinsic supersymmetry of the coupling to a PT-supersymmetry, whose corresponding pseudo-supersymmetry, in the absence of the Coulomb term, is easily identified. In the latter case, solutions of the problem can be obtained, in a simple manner, from those of the non-deformed Dirac oscillator using a similarity inter-transformation.