Improved energy spectra of the Klein–Gordon and Schrödinger equations under the Tietz potential by WKB and super-symmetric WKB methods

Abstract

The relative convergence of the WKB and the Super-symmetric WKB (SWKB) approximations are studied with the hyper-radial Klein–Gordon and Schrodinger equations under the molecular Tietz potential. We used a Pekeris approximation to deal with the orbital centrifugal barrier energy. The variations of the energy levels with the potential parameters are investigated. The results revealed that the SWKB energy modeled for a hypothetical system is exact and nearly indistinguishable from the usual WKB energy. Both the WKB and SWKB approach give better results of the energy levels compared to the results obtained by other analytical methods such as the parametric Nikiforov–Uvarov (NU) and the improved asymptotic iteration (AIM) used with the Greene–Aldrich approximation for the centrifugal energy. For the s-wave case , the SKWB energy coincides with the NU and AIM obtained values whereas the WKB energy fluctuates slightly due to the effect of regularization of the orbital centrifugal barrier. Furthermore, the obtained energy eigenvalues for CO and LiH diatomic molecules are in excellent agreement with the results in the existing literature.