Solutions of the Non-relativistic Equation Interacting with the Varshni-Hellmann Potential Model with Some Selected Diatomic Molecules

Abstract

The approximate solutions of Schrödinger equation for the newly proposed
Varshni-Hellmann potential (VHP) are obtained within the framework of the NikiforovUvarov method by employing the Greene-Aldrich approximation scheme to deal with the
centrifugal term. The numerical results of the ro-vibrational energies and normalized
wavefunction in closed form are obtained in terms of Jacobi polynomials for various
quantum states of the diatomic molecules of LiH an , TiH, CrH d ScN, respectively.
Four special cases of the potential are also studied and their numerical energy eigenvalues
evaluated are in agreement with those reported in the existing literature. Also, the behavior
of the energy spectra for the ground state of the selected diatomic molecules is illustrated
graphically.