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


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IKHDAİR S., Sever R.

ANNALEN DER PHYSIK, vol.17, no.11, pp.897-910, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 11
  • Publication Date: 2008
  • Doi Number: 10.1002/andp.200810322
  • Journal Name: ANNALEN DER PHYSIK
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.897-910
  • Keywords: Bound states, Manning-Rosen potential, Nikiforov-Uvarov method, KLEIN-GORDON EQUATION, SPIN-ZERO PARTICLE, BOUND-STATES, POLYNOMIAL SOLUTION, DIATOMIC-MOLECULES, INTEGRAL TREATMENT, PLUS, OSCILLATOR, VIBRATIONS, MECHANICS

Abstract

The Schrodinger 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 1, 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 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 Hulthen potential case.