Expectation Values and Energy Spectra of the Varshni Potential in Arbitrary Dimensions

Abstract

The Klein-Gordon equation with Varshni potential was solved through the Nikiforov-Uvarov method. The Greene and Aldrich approximation schemes were employed to overcome the centrifugal barrier. The energy eigenvalues were obtained in relativistic and non-relativistic regimes, as well as the corresponding normalized wave functions. Energy spectra and expectation values of the square of inverse of position (r^-2) kinetic energy (T) and the square of the momentum (p² ) for five selected diatomic molecules: H₂, HCl, TiH, I² and CO, using their separate spectroscopic parameters were computed through Hellmann-Feynman Theorem. Bound-state energy eigenvalues were also  computed for Varshni potential and the numerical results agree with the already existing literature.

Keywords: Expectation values, Varshni potential, Nikiforov-Uvarov method, KleinGordon equation.