Z. Naturforsch. 68a, 499 – 509
Shape-Invariant Approach to Study Relativistic Symmetries of the Dirac Equation with a New Hyperbolical Potential Combination
1 Theoretical Physics Group, Department of Physics, University of Uyo, Nigeria
2 Department of Physics, Shahrood University of Technology, P.O.Box 3619995161-316, Shahrood, Iran
3 Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran
Received December 4, 2012 / revised February 22, 2013 / published online May 22, 2013
Spin and pseudospin symmetries of the Dirac equation are investigated for a novel interaction term, i. e. the combination of Tietz plus a hyperbolical (Schiöberg) potential besides a Coulomb tensor interaction. This choice of interaction yields many of our significant terms in its special cases. After applying a proper hyperbolical term, we find the corresponding superpotential and thereby construct the partner Hamiltonians which satisfy the shape-invariant condition via a translational mapping. We report the spectrum of the system and comment on the impact of various terms engaged.
Key words: Dirac Equation; Tietz Potential; Hyperbolical Potential; Supersymmetry Quantum Mechanics; Shape Invariant.
PACS numbers: 03.65Ge; 03.65Pm; 03.65Db