Numerical determination of energy eigenvalues for bound states of the Manning-Rosen potential using the shooting method

Energy eigenvalues of the non-relativistic Schrödinger equation with the exponential-type Manning–Rosen (MR) potential are calculated numerically for different screening parameters using the shooting method and the Numerov method. The energy eigenvalues calculated for nonzero angular momentum states are found to be more accurate than the values previously obtained numerically by other authors. Therefore, the energy eigenvalues derived in this study should be used as reference values for validation of semi analytical methods regarding the Manning Rosen potential and the Hulthén potential.