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Global Journal of Human Social Science

Solutions of the Relativistic and Non-Relativistic Wave Equations with la0 for Modified Hylleraas Plus Attractive Radial Molecular Potential using Nikiforov-Uvarov Method

Pigwe Isa Amos, Louis Hitler

Published May 4, 2018• 0 citations
OpenAlex

Abstract

It is well known that the exact solutions play an important role in quantum mechanics since they contain all the necessary information regarding the quantum model under study. However, the exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest. In this paper, bound state solutions of the Schrodinger and Klein-Gordon equations with Modified Hylleraas plus attractive radial potentials (MHARP), have been obtained using the parametric Nikiforov-Uvarov (NU) method which is based on the solutions of general second-order linear differential equations with special functions. The bound state eigen energy solutions for both wave equations were obtained. Also special cases of the potential have been considered and their energy eigen values obtained.

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It is well known that the exact solutions play an important role in quantum mechanics since they contain all the necessary information regarding the quantum model under study. However, the exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest. In this paper, bound state solutions of the Schrodinger and Klein-Gordon equations with Modified Hylleraas plus attractive radial potentials (MHARP), have been obtained using the parametric Nikiforov-Uvarov (NU) method which is based on the solutions of general second-order linear differential equations with special functions. The bound state eigen energy solutions for both wave equations were obtained. Also special cases of the potential have been considered and their energy eigen values obtained.
In this work, we obtained an approximate bound state solution to Schrodinger with Hulthen plus exponential Coulombic potential with centrifugal potential barrier using parametric Nikiforov-Uvarov method.We obtained both the eigen energy and the wave functions to non -relativistic wave equations.We implement Matlab algorithm to obtained the numerical bound state energies for various values of adjustable screening parameter at various quantum state..The developed potential reduces to Hulthen potential and the numerical bound state energy conform to that of existing literature.
We study the nonrelativistic Schrödinger equation for q-deformed Hulthen plus modified inversely quadratic Yukawa potential using the generalized parametric form of NIkiforov-Uvarov method. The energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric function are obtained. We have also discussed four (4) special cases of this potential, i.e. Woods-Saxon, Hulthen, Morse and inversely quadratic potentials. Keywords: Nonrelativistic Schrödinger equation, q-deformed Hulthen potential, modified inversely quadratic Yukawa potential, parametric Nikiforov-Uvarov method.
We have obtained approximate bound state solutions of Schrödinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.