Solution of the Schrödinger equation with inversely quadratic Yukawa potential (IQYP) plus Kratzer-Fues (KFP) potential using the WKB quantum mechanical formalism

Benedict Iserom Ita,Hitler Louis,Nelson Nzeata-Ibe

doi:10.26850/1678-4618eqj.v44.3.2019.p50-55

Benedict Iserom Ita, Hitler Louis + Show 1 more

Open Access

https://doi.org/10.26850/1678-4618eqj.v44.3.2019.p50-55

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Journal: Ecletica Quimica	Publication Date: Jul 4, 2019
Citations: 4	License type: CC BY 4.0

Affiliation: University of Calabar

Abstract

The main objective of this research work is theoretical investigate the bound state solutions of the non-relativistic Schrödinger equation with a mixed potential composed of the Inversely Quadratic Yukawa/Attractive Coulomb potential plus a Modified Kratzer potential (IQYCKFP) by utilizing the Wentzel-Kramers-Brillouin (WKB) quantum theoretical formalism. The energy eigenvalues and its associated wave functions have successfully been obtained sequel to certain diatomic molecules includes; HCL, HBr, LiH.

Highlights

One of the interesting problems in quantum mechanics is to get exact solutions of the Schrӧdinger equation.To do this, a real potential is often selected to serve as the driving force of the energy eigenvalues and the eigenfunctions of the Schrӧdinger equation[1,2,3]
The main objective of this research work is theoretical investigate the bound state solutions of the nonrelativistic Schrödinger equation with a mixed potential composed of the Inversely Quadratic Yukawa/Attractive Coulomb potential plus a Modified Kratzer potential (IQYCKFP) by utilizing the Wentzel-Kramers-Brillouin (WKB) quantum theoretical formalism
The energy eigenvalues and its associated wave functions have successfully been obtained in sequel to certain diatomic molecules includes; HCL, HBr, LiH

Summary

Introduction

One of the interesting problems in quantum mechanics is to get exact solutions of the Schrӧdinger equation. A real potential is often selected to serve as the driving force of the energy eigenvalues and the eigenfunctions of the Schrӧdinger equation[1,2,3]. These state solutions reveal the particle dynamics in nonrelativistic quantum mechanics[2]. Numerous researchers have investigated the bound states of the Schrӧdinger equation using variety of potentials and quantum formalism. Some of these potentials play critical roles in many fields of Physics such as Molecular Physics, Solid State and Chemical Physics[4]. In this work, using the Wentzel, Kramers and Brillouin (WKB) quantum approximation, we shall investigate the bound state solutions of the Schrӧdinger equation using a combination of potentials known as the Inversely Quadratic Yukawa/Attractive Coulomb potential plus a Modified Kratzer potential (IQYCKFP)

The WKB Theoretical Approximation

Solutions of the Schrödinger Equation

Conclusions