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

Abstract

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 ⟨ −2 ⟩, ⟨ −1 ⟩, ⟨ ⟩, and ⟨ 2 ⟩ for four different diatomic molecules: hydrogen molecule (H 2 ), 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.

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

“…which is good agreement with the result in Equation ( 28) (If B and C are considered zero as a special case) of Ref [31]. Generally, it is obviously seen from Equation.…”

“…Nonetheless, Okon et al reported analytical solutions of the Schrödinger equation for the Hulthén-Yukawa plus inversely quadratic potential. [31] In Ref. [32][33][34][35][36][37][38][39], the scalar potential, which is nonequal and equal to the vector potential, was supposed to get the bound states of the KFG equation for some typical potential from the ordinary quantum mechanics.…”

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

“…The NU method is based on reducing second order linear differential equation to a generalised equation of hyper-geometric type and provides exact solutions in terms of special orthogonal functions like Jacobi and Laguerre as well as corresponding energy eigenvalues 73 – 78 . The standard differential equation for parametric NU method according to Tezcan and Sever 79 is given as The parametric constants are obtained as follows The condition for energy equation is given as The corresponding total wave function is then given as …”

Eigen-Solutions to Schrodinger Equation with Trigonometric Inversely Quadratic Plus Coulombic Hyperbolic Potential

“…Eigen-solutions to relativistic and nonrelativistic wave equations has been of growing interest for decades because of its applications to some physical systems. The Schrodinger wave equation constitute the nonrelativistic wave equation while Klein-Gordon and Dirac constitutes the relativistic wave equations [1][2][3][4][5][6][7][8]. Most potentials are modelled and applied to solve some physical systems examples include: Morse potential, Tietz-Wei, pseudoharmonic, Deng-Fan, Kratzer -Feus, Mie-Type and many of exponential -type potentials [9][10][11][12][13][14][15].…”