https://doi.org/10.1140/epjd/s10053-022-00507-2
Regular Article - Atomic Physics
The influence of external magnetic and Aharonov–Bohm flux fields on bound states of the Klein–Gordon and Schrodinger equations via the SWKB approach
1
Department of Physics, Federal University of Petroleum Resources, 330102, Effurun, Delta State, Nigeria
2
Theoretical Physics Group, Department of Physics, University of Uyo, 520101, Uyo, Nigeria
3
Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, Nigeria
4
Department of Physics, School of Basic Sciences, Nigeria Maritime University, P.M.B. 1005, Okerenkoko, Warri, Delta State, Nigeria
5
Department of Physics, Federal University of Technology Owerri, P.M.B.1526, Ihiagwa, Owerri, Imo State, Nigeria
6
Department of Physics and Engineering Sciences, Buein Zahra Technical University, Qazvin, Iran
7
Department of Physics, Kogi State University, Anyigba, Nigeria
Received:
29
January
2022
Accepted:
15
September
2022
Published online:
30
September
2022
We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving in a quantum mechanical solvable potential under the influence of the external magnetic and Aharonov–Bohm flux fields. We utilized the supersymmetric WKB approach to obtain both the energy levels and normalized wave function in closed form. The proposed potential reduces to the screened Kratzer, Kratzer, Yukawa and Coulomb potential functions as special cases and admits the corresponding energy eigenvalues in both relativistic and non-relativistic regimes. When the external magnetic and Aharonov–Bohm flux fields were turned off, the relativistic, non-relativistic energies and ground state probability density overlap for the magnetic quantum numbers (
). The presence of the fields removes the degeneracy and shifts the energy levels of the Klein–Gordon particle. However, we found that the magnetic field strength has no effects on the maximum non-relativistic energy. Generally, the results are consistent with the works in existing literature where the authors utilized different forms of potential energy functions.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
