Corrected analytical solution of the generalized Woods–Saxon potential for arbitrary $\ell $ states

The bound state solution of the radial Schrodinger equation with the generalized Woods–Saxon potential is carefully examined using the Pekeris approximation for arbitrary states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different n and quantum numbers. The closed forms obtained are applied to calculate the single particle energy levels of a neutron orbiting around 56Fe nucleus in order to check the consistency between the analytical and the Gamow code results. The analytical results are in good agreement with the results obtained using Gamow code for .