An-Najah Staff

We solve the parametric generalized effective Schrödinger equation with a specific choice of position-dependent mass function and Morse oscillator potential by means of the Nikiforov–Uvarov method combined with the Pekeris approximation scheme. All bound-state energies are found explicitly and all corresponding radial wave functions are built analytically. We choose the Weyl or Li and Kuhn ordering for the ambiguity parameters in our numerical work to calculate the energy spectrum for a few (H₂, LiH, HCl and CO) diatomic molecules with arbitrary vibration n and rotation l quantum numbers and different position-dependent mass functions. Two special cases including the constant mass and the vibration s-wave (l = 0) are also investigated.

The approximated energy eigenvalues and the corresponding eigenfunctions of the spherical Woods-Saxon effective potential in D dimensions are obtained within the new improved quantization rule for all l-states. The Pekeris approximation is used to deal with the centrifugal term in the effective Woods-Saxon potential. The inter-dimensional degeneracies for various orbital quantum number l and dimensional space D are studied. The solutions for the Hulth\'{e}n potential, the three-dimensional (D=3), the -wave (l=0) and the cases are briefly discussed.