Studies on bound-state spectra of Manning-Rosen potential

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral method. \emph{All} 55 eigenstates with $n \leq 10$ are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a \emph{non-uniform, optimal} spatial radial discretization. A detailed investigation has been made on energy changes with respect to \emph{screening and other} potential parameters. A systematic estimation of \emph{critical} screening parameters are given for these eigenstates. Special emphasis has been given to \emph{higher} states and in the vicinity of \emph{critical screening} region. A thorough comparison with literature results is made wherever possible. This \emph{surpasses} the accuracy of \emph{all} other existing methods currently available. Several \emph{new} states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered.