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Revista Mexicana de Física

Bound state solutions of schrodinger equation with modified hylleraas plus exponential rosen morse potential

A. N. Ikot, Akaninyene Daniel Antia, I. O. Akpan, Oladunjoye A. Awoga

Published Jan 1, 2013• 9 citations
OpenAlex

Abstract

"We present solutions of the Schrödinger equation with modified Hylleraas plus exponential Rosen Morse potential within the framework of the elegant approximation to deal with the centrifugal term for arbitrary orbital angular quantum number. We obtain the energy spectrum and the corresponding wave function using the parametric form of the Nikiforov-Uvarov method. In many cases of interest the energy eigenvalues and eigen functions have been discussed for different potentials."

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"We present solutions of the Schrödinger equation with modified Hylleraas plus exponential Rosen Morse potential within the framework of the elegant approximation to deal with the centrifugal term for arbitrary orbital angular quantum number. We obtain the energy spectrum and the corresponding wave function using the parametric form of the Nikiforov-Uvarov method. In many cases of interest the energy eigenvalues and eigen functions have been discussed for different potentials."
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are 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.
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 paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.