The numerical results of two of the potentials are compared to that of existing literature. In Section 4, we have deductions of three well-known potentials from the proposed potential. In Section 3, we presented the radial solution to Schrodinger wave equation using the proposed potential and obtained both the energy eigenvalue and their corresponding normalized wave function. Section 1 is the introduction Section 2 is the brief introduction of conventional Nikiforov-Uvarov method. This article is divided into seven sections. These potentials are studied with some specific methods and techniques like the following: asymptotic iteration method, Nikiforov-Uvarov method, supersymmetric quantum mechanics approach, formular method, exact quantisation, and many more. Other potentials have been used in studying bound state solutions like the following: Hulthen, Poschl-Teller, Eckart, Coulomb, Hylleraas, pseudoharmonic, and scarf II potentials and many others. The quantum interaction potential (HYIQP) can be used to compute the bound state energies for both homonuclear and heteronuclear diatomic molecules. Bound state solutions predominantly have negative energies because the energy of the particle is less than the maximum potential energy. Schrodinger wave equations constitute nonrelativistic wave equation while Klein-Gordon and Dirac equations constitute the relativistic wave equations. Bound state solutions of relativistic and nonrelativistic wave equation arouse a lot of interest for decades. Diatomic molecules contains two atoms per molecule and can either be homonuclear if it contains two atoms of the same kind per molecule or be heteronuclear if its contains two atoms of different kind per molecule. The excitation of atoms of some diatomic molecules especially the homonuclear diatomic molecules is the principle used in spectrophotometric technique. The study of diatomic molecules is very significant and applicable in many areas of chemical and physical sciences. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.
![schrodinger equation schrodinger equation](https://upload.wikimedia.org/wikipedia/commons/5/53/Schrodinger_Equation.png)
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. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature.
![schrodinger equation schrodinger equation](https://www.researchgate.net/publication/343717373/figure/fig1/AS:933785461858305@1599643211586/Fundamental-solutions-of-stationary-Schroedinger-equation-for-barriers-of-given-shape.png)
The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. We employed Hellmann-Feynman Theorem (HFT) to compute expectation values, ,, and for four different diatomic molecules: hydrogen molecule (H 2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. We obtained the energy eigenvalues and the total normalized wave function.
![schrodinger equation schrodinger equation](https://inteng-storage.s3.amazonaws.com/images/JULY/sizes/Schrodinger_cat_equation_resize_md.jpg)
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).