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 Nikiforov-Uvarov 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 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. Keywords: Schrödinger equation; Varshni-Hellmann potential, Nikiforov-Uvarov method, Diatomic molecules.