Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT) to compute expectation values r-2, r-1, T, and p2 for four different diatomic molecules: hydrogen molecule (H2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

Spectroscopic constants and potential-energy derivatives for diatomic molecules of alkali halides

The potential-energy derivatives are derived directly from the experimental values of the spectroscopic constants for diatomic alkali halides. It is found that these derivatives are useful in predicting more accurately the values of the higher order spectroscopic constant (βe). Some interesting new relations showing the dependence of the potential-energy derivatives on internuclear distances have been investigated empirically. An attempt has been made to interpret these relations on the basis of interionic potentials.