Approximate \(l\)-states of the Manning-Rosen potential by using Nikiforov-Uvarov method. (English) Zbl 1244.81019
Summary: The approximately analytical bound state solutions of the \(l\)-wave Schrödinger 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 principal and orbital quantum numbers \(n\) and \(l\) with two different values of the potential screening parameter \(a\). It is found that our results are in good agreement with the those obtained by other methods for short potential range, lowest values of orbital quantum number \(l\), and \(a\). Two special cases of much interest are investigated like the \(s\)-wave case and Hulthén potential case.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
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