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

References in corpus (4)

• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• Relativistic treatment in D-dimensions to a spin-zero particle with noncentral equal scalar and vector ring-shaped Kratzer potential

Cited by in corpus (4)

• An improved approximation scheme for the centrifugal term and the Hulthen potential
• Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
• Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials
• Exact Quantization Rule to the Kratzer-Type Potentials: An Application to the Diatomic Molecules