https://doi.org/10.1140/epjp/s13360-024-05375-w
Regular Article
Geometric topological effect on non-relativistic solution under pseudoharmonic and extended double ring-shaped potentials
1
Laboratory System Dynamical and Control, University Larbi Ben M’hidi, Oum El-Bouaghi, Algeria
2
Department of Mathematics and Computer Science, University Larbi Ben M’hidi, Oum El-Bouaghi, Algeria
3
Natural Sciences and Materials Laboratory, University Center Abdelhafid Boussouf, Mila, Algeria
4
Department of Mathematics, Institute of Mathematics and Computer Science, University Center Abdelhafid Boussouf, Mila, Algeria
5
Department of Physics, University of Science & Technology Meghalaya, 793101, Ri-Bhoi, India
b
b.boudjedaa@centre-univ-mila.dz
Received:
16
March
2024
Accepted:
17
June
2024
Published online:
5
July
2024
In this paper, we address the non-relativistic wave equation governed by the Schrödinger equation, exploring its behavior under the influence of radial and angular dependent potentials within a topological defect geometry. Our primary focus is on investigating quasi-exactly solvable problems within the framework of topological defect geometry background. We specifically employ the pseudoharmonic potential as the radial component and an extended ring-shaped potential as the angular dependent component. To tackle the problem, we utilize the Bethe ansatz method to determine solutions of the angular parts of the wave equation, while solving the radial wave equation through the biconfluent Heun equation. Our results demonstrate an interplay between the eigenvalue solution of quantum particles and the topological defect, leading to modifications in the result compared to solutions obtained in the flat space. Additionally, the presence of pseudoharmonic potential and the eigenvalue contribution from the angular equations further influence the quantum system’s eigenvalue solution overall.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) 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.
