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

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 $\alpha .$ 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 $(n,l,D)\to (n,l\pm 1,D\mp 2)$. This solution reduces to the Hulthén potential case.

25 pages

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Cited by in corpus (12)

• Rotation and vibration of diatomic molecule in the spatially-dependent mass Schrodinger equation with generalized q-deformed Morse potential
• An improved approximation scheme for the centrifugal term and the Hulthen potential
• On the bound-state solutions of the Manning-Rosen potential including improved approximation to the orbital centrifugal term
• Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
• Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials
• Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
• Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems
• Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method
• Ro-vibrational energy analysis of Manning-Rosen and Pöschl-Teller potentials with a new improved approximation in the centrifugal term
• Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials
• Analytical approximate bound state solution of Schrödinger equation in $D$-dimensions with a new mixed class of potential for arbitrary $\ell$-state via asymptotic iteration method
• Exact Quantization Rule to the Kratzer-Type Potentials: An Application to the Diatomic Molecules