Eur. Phys. J. A (2016) 52: 201
https://doi.org/10.1140/epja/i2016-16201-4

Regular Article - Theoretical Physics

Relativistic Killingbeck energy states under external magnetic fields

¹ Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
² Faculty of Physics, Semnan University, Semnan, Iran
³ Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine
⁴ Department of Electrical Engineering, Near East University, Mersin 10, Nicosia, Northern Cyprus, Turkey

^* e-mail: eshgi54@gmail.com

Received: 21 March 2016
Revised: 21 June 2016
Accepted: 3 July 2016
Published online: 22 July 2016

Abstract

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun's differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states.