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arXiv:0811.3626 · Physica Scripta

The Hulthén potential in D-dimensions

D. Agboola

Published Dec 1, 2009• 59 citations
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Abstract

An approximate solution of the Schrödinger equation with the Hulthén potential is obtained in D-dimensions with an exponential approximation of the centrifugal term. A solution to the corresponding hyperradial equation is given by using the conventional Nikiforov–Uvarov method. The normalization constants for the Hulthén potential are also computed. The expectation values ⟨r −2⟩, ⟨V(r)⟩ are also obtained by using the Hellmann–Feynman theorem.

DOI
10.1088/0031-8949/80/06/065304

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In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

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arXiv:quant-ph/0508009•Aug 1, 2005•6 citations
An approximate solution of the Schrödinger equation with the Hulthén potential is obtained in D-dimensions with an exponential approximation of the centrifugal term. A solution to the corresponding hyperradial equation is given by using the conventional Nikiforov–Uvarov method. The normalization constants for the Hulthén potential are also computed. The expectation values ⟨r −2⟩, ⟨V(r)⟩ are also obtained by using the Hellmann–Feynman theorem.
The Schrödinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions).The Nikiforov-Uvarov (NU) method is used in the calculations.We present numerical calculations of energy eigenvalues to two-and four-dimensional systems for arbitrary quantum numbers n and l with three different values of the potential parameter α.It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional sytem from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation (n, l, D) → (n, l ± 1, D ∓ 2)..This solution reduces to the Hulthén potential case.
In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.