Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equa
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ORIGINAL PAPER
Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential Benedict I. Ita 1 & Hitler Louis 1
&
Emmanuel I. Ubana 1 & Philemena E. Ekuri 1 & Chinedu U. Leonard 2 & Nelson I. Nzeata 1
Received: 3 July 2020 / Accepted: 28 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1. Keywords Schrodinger . Eckart . Inversely quadratic . Parametric Nikiforov-Uvarov method . Diatomic molecules
Introduction Recently, much attention has been drawn towards the Eckarttype potential model as a molecular potential model due to its wide applications in physics and chemical physics [1]. It is expressed as
−η
e−∝r e−∝r þζ −∝r ð1−e Þ ð1−e−∝r Þ2
ð1Þ
where ζ and η are the potential depths of the Eckart potential and α is an adjustable positive screening parameter. Sari et al. in 2015 studied the analytical approximations to the bound state solutions of the Dirac equation with the Eckart potential by using the asymptotic method [2]. Also the l-wave * Hitler Louis [email protected] 1
Physical and Quantum Chemistry Research Group, Department of Pure and Applied Chemistry, Faculty of Physical Sciences, University of Calabar, Calabar P.M.B 1115, Nigeria
2
Department of Computer Science, Faculty of Physical Sciences, University of Calabar, Calabar P.M.B 1115, Nigeria
scattering state solutions of the Schrödinger equation for the Eckart potential has been studied analytically by using this same approximation scheme proposed by Greene and Aldrich [3, 4]. Ikhdair and colleagues solved the Ddimensional radial Klein-Gordon equation for any orbital angular momentum quantum number and for the scalar and vector Eckart-type exponential potentials using a general mathematical model of the Nikiforov-Uvarov method [5]. Hassanabadi et al. in 2013 obtained the bound state solutions by studying the s-wave Klein–Gordon equation with equally mixed Eckart potentials [6]. Zhang in 2008 investigated the bound state solutions of the Klein–Gordon equation with equal vector and scalar Eckart potentials using the approximation for the centrifugal term proposed by Greene and Aldrich for any orbi
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