Analytical investigation of spin-orbit interaction effect on Hulthen potential model using perturbation theory

Edet Asuquo Thompson, Samuel Inyang

Abstract

Abstract: This study investigates the effect of Spin-Orbit interaction on Hulthén potential model within the non-relativistic quantum mechanical domain. The Schrödinger equation is solved for a particle with spin degree of freedom moving in a central force field modelled by the Hulthén potential. The Spin-Orbit interaction is viewed as a form of perturbation. Hence the perturbation theory is applied to correct the energy eigenvalues of the Hulthén system, thereby revealing the effect of Spin-Orbit effect. The results of this study shows that the energy levels of the Hulthén potential splits according to the j = ℓ ± 1⁄2 scheme except for ℓ = 0. This makes the Hulthén potential model suitable for a system with spin degree of freedom within the non-relativistic quantum mechanics. Also, Schrödinger equation which is apt for a spinless particle can be applied to study a system with spin degree of freedom by treating the Spin-Orbit interaction as a form of perturbation.

Keywords

Schrodinger equation; Hulthen potential; perturbation theory; Spin-orbit interaction; energy eigenvalues

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DOI: https://doi.org/10.20961/jphystheor-appl.v10i1.114129

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