Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method

Details Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method

2011-10-14

arxiv.org/abs/1110.3153v1

ISRN-Math. Phys., v..2012 (2012) 201525-20

Physics

Mathematical Physics

21 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:0909.0623

Scientific paper

10.5402/2012/201525

The approximately analytical bound state solutions of the l-wave Schr\"odinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter {\alpha}. It is found that our results are in good agreement with the those obtained by other methods for short potential range, small l and {\alpha}. Two special cases are investigated like the s-wave case and Hulth\'en potential case.

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