The influence of external magnetic and Aharonov–Bohm flux fields on bound states of the Klein–Gordon and Schrodinger equations via the SWKB approach

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 76; no. 9
• Main Authors: Omugbe, E., Osafile, O. E., Okon, I. B., Okorie, U. S., Suleman, K. O., Njoku, I. J., Jahanshir, A., Onate, C. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022; Springer Nature B.V
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Coulomb potential; Eigenvalues; Energy levels; Field strength; Molecular; Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Potential energy; Quantum Information Technology; Quantum mechanics; Quantum numbers; Quantum Physics; Regular Article - Atomic Physics; Relativistic effects; Schrodinger equation; Spectroscopy/Spectrometry; Spintronics; Wave functions
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/s10053-022-00507-2

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 ( m = - 1 , 1 ). 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. Graphical abstract