# Expectation Values of Some Diatomic Molecules With Quantum Interaction Potential In Schrodinger Equation with Hellmann-Feynman Theorem Via Conventional Nikiforov-Uvarov Method

## TL;DR

This paper calculates bound state energies and expectation values for specific diatomic molecules using the Schrödinger equation with a combined potential, employing the Nikiforov-Uvarov method and Hellmann-Feynman theorem.

## Contribution

It introduces a novel application of the Nikiforov-Uvarov method to the HYIQP potential for diatomic molecules and computes expectation values with numerical and graphical methods.

## Key findings

- Energy eigenvalues for H2, LiH, HCl, CO calculated.
- Wave functions and probability densities obtained.
- Potential reduces to known potentials in special cases.

## Abstract

In this work, we used a tool of conventional Nikiforov-Uvarov method to determine bound state solution of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigen values and the total wave function . We employed Hellmann-Feynmann Theorem (HFT) to compute expectation values 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: Hulthen potential, Yukawa potential and inversely quadratic potential. 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 a mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

---
Source: https://tomesphere.com/paper/1702.03923