Physics – Quantum Physics
Scientific paper
2011-04-02
Phys. Scr. 83 (2011) 015010 (10pp)
Physics
Quantum Physics
21 pages
Scientific paper
10.1088/0031-8949/83/01/015010
The approximate analytical bound state solution of the Schr\"odinger equation for the Manning-Rosen potential is carried out by taking a new approximation scheme to the orbital centrifugal term. The Nikiforov-Uvarov method is used in the calculations. We obtain analytic forms for the energy eigenvalues and the corresponding normalized wave functions in terms of the Jacobi polynomials or hypergeometric functions for different screening parameters 1/b. The rotational-vibrational energy states for a few diatomic molecules are calculated for arbitrary quantum numbers n and l with different values of the potential parameter {\alpha}. The present numerical results agree within five decimal digits with the previously reported results for different 1/b values. A few special cases of the s-wave (l=0) Manning-Rosen potential and the Hulth\'en potential are also studied. Keywords: Energy eigenvalues; Manning-Rosen potential; Nikiforov-Uvarov method, Approximation schemes. 03.65.-w; 02.30.Gp; 03.65.Ge; 34.20.Cf
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