1207.5135 (B. J. Falaye et al.)

Any $\ell$ -state solutions of the Schrödinger equation for the
Manning-Rosen potential via asymptotic iteration method    [PDF]

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

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.

View original: http://arxiv.org/abs/1207.5135