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arXiv · 1207.5135

Bound state solutions of the Manning-Rosen potential

B. J. Falaye·K. J. Oyewumi·T. T. Ibrahim·M. A. Punyasena·C. A. Onate
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Abstract

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\ell$-wave solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers $n$ and $\ell$ for some diatomic molecules (HCl, CH, LiH and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulth$\acute{e}$n potential case are also presented.

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B. J. Falaye, K. J. Oyewumi, T. T. Ibrahim, M. A. Punyasena, C. A. Onate. 2012-07-21. Bound state solutions of the Manning-Rosen potential. https://doi.org/10.1139/cjp-2012-0330

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