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

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

2008-01-23

arxiv.org/abs/0801.3518v1

Physics

Quantum Physics

25 pages

Scientific paper

10.1002/andp.200810322

The Schr\"{o}dinger 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 Hulth\'{e}n potential case.

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