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arXiv:0801.3518 · Annalen der Physik

Approximate l-state solutions of the D-dimensional Schrödinger equation for Manning-Rosen potential

Sameer M. Ikhdair, R. Sever

Published Aug 15, 2008• 51 citations
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Abstract

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.

DOI
10.1002/andp.200810322

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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.
Abstract 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 system 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.
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.
In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.
The Schrödinger equation under the ManningRosen potential is solved in arbitrary dimension via the quantum mechanical idea of supersymmetry.The Pekeris approximation is used to overcome the inconsistency of the potential with the centrifugal term.Comments on the energy eigenvalue behavior versus dimension are included.The inter-dimensional degeneracy for various orbital quantum number l and dimensions D are studied.The expectation values of some physical parameters are reported via the FeynmanHellmann theorem.
We solved the Schrödinger equation with a certain approximation to the centrifugal term for an arbitrary angular momentum state with the Eckart Manning Rosen potential. The bound-state energy eigenvalues and the corresponding wave functions have been approximately obtained using the parametric Nikiforov Uvarov method. The solutions of the Schrödinger equation for the Eckart potential, Manning Rosen potential, and Hulthén potential have been obtained using a certain transformation. The concepts of the Shannon entropy and the Fisher information of a system under the Eckart Manning Rosen potential are investigated in detail. The behavior of the screening parameter and the quantum number n for Fisher information and the Shannon entropy are also investigated.