Hellmann Potential in Spinless Salpeter Equation with  Potential Barrier within the Framework of Nikiforov-Uvarov method

Akaninyene Daniel Antia

doi:10.17951/aaa.2016.71.53

Abstract

<p>In this paper, we have solved the spinless Salpeter equation (SSE) with Hellmann potential under the framework of NIkiforov-Uvarov (NU) method. The energy eigenvalues and corresponding wave functions for this system express in terms of the Jacobi polynomial are also obtained. With the help of approximation scheme the potential barrier has been evaluated. The results obtained in this work would have many applications in nuclear physics, chemical physics, atomic and molecular physics, molecular chemistry and other related areas as the results under limiting cases could be used to study the binding energy and interaction of some diatomic molecules. As a guide to interested readers, we have provided numerical data which discuss the energy spectra for this system.</p><p> </p>

Highlights

There has been an increasing interest in finding the analytical solutions of wave equations in relativistic and non-relativistic quantum mechanics such as Schrödinger, Klein-Gordon, Dirac, Duffin Kemmer-Petian (DKF) and Spinless Bethe-Salpeter equation with different potential models [1,2,3,4,5,6,7,8]
The Bethe-Salpeter equation is the semi-relativistic equation that describes the bound states of a two body quantum field system in a relativistic covariant formalism [10]
The spinless Salpeter Equation (SSE) is a generalization of Schrödinger equation in the quantum relativistic regime [11]

Summary

INTRODUCTION

There has been an increasing interest in finding the analytical solutions of wave equations in relativistic and non-relativistic quantum mechanics such as Schrödinger, Klein-Gordon, Dirac, Duffin Kemmer-Petian (DKF) and Spinless Bethe-Salpeter equation with different potential models [1,2,3,4,5,6,7,8]. Zarrinkamar et al, [14] studied the two body Salpeter equation with exponential potential using SUSYQM method. The aim of this work is to solve the SSE equation for the Hellmann potential and to calculate the energy eigenvalues and the corresponding wavefunctions which are expressed in terms of Jacobi polynomials for any arbitrary l state using a suitable approximation scheme. The NU method was presented by Nikiforov and Uvarov [24] and has been employed to solve second order differential equations such as Schrödinger wave equation (SWE), Klein-Gordon equation (KGE), Dirac equation (DE) etc. According to NU method, the energy eigenvalue equation and eigenfunction respectively satisfy the following sets of equation, c2n 2n 1c5 2n 1 c9 c3 c8 nn 1c3 c7 2c3c8 2 c8c9 0 (5)

TWO-BODY SPINLESS SALPETER EQUATION

CONCLUSION