Topological Effects on Non-Relativistic Eigenvalue Solutions Under AB-Flux Field with Pseudoharmonic- and Mie-type Potentials

• URL: http://arxiv.org/abs/2210.04617v1
• Date: Tue, 4 Oct 2022 04:56:43 GMT
• Title: Topological Effects on Non-Relativistic Eigenvalue Solutions Under AB-Flux Field with Pseudoharmonic- and Mie-type Potentials
• Authors: Faizuddin Ahmed
• Abstract summary: We investigate the quantum dynamics of a Schr"odinger particle confined by the Aharonov-Bohm flux field. We show that the eigenvalue solutions shift more due to the magnetic flux in addition to the topological defects.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we investigate the quantum dynamics of a Schr\"{o}dinger particle confined by the Aharonov-Bohm flux field with pseudoharmonic-type potential under topological defects produced by a point-like global monopole. We solve the three-dimensional radial Schr\"{o}dinger wave equation analytically and determine the exact eigenvalue solution of the quantum system. Afterwards, we consider Mie-type potential in the quantum system and solve the radial Schr\"{o}dinger equation analytically. We then analyze the effects of topological defects of the geometry and the magnetic flux field with these potentials on the eigenvalue solutions. We show that the eigenvalue solutions shift more due to the magnetic flux in addition to the topological defects which gives an analogue of the Aharonov-Bohm effect for the bound state. Finally, we utilize the eigenvalue solutions to some diatomic molecular potentials of physical interest and analyze the topological effects and the magnetic flux field on them.

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