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International Journal of Recent advances in Physics

Bound- State Solution of Schrodinger Equation with Hulthen Plus Generalized Exponential Coulomb Potential Using NIKIFOROV-UVAROV Method

I. B. Okon, Oyebola O. Popoola

Published Aug 31, 2015• 13 citations
Publisher

Abstract

We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equation with Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method.Using this method, we obtained the energy-eigen value and the total wave function.We implement C++ algorithm, to obtained the numerical values of the energy for different quantum state starting from the first excited state for different values of the screening parameter.

DOI
10.14810/ijrap.2015.4301

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We apply an approximation to centrifugal term to find bound state solutions to Schrodinger equation with Hulthen Plus generalized exponential Coulomb potential Using Nikiforov-Uvarov Method.Using this method, we obtained the energy-eigen value and the total wave function.We implement C++ algorithm, to obtained the numerical values of the energy for different quantum state starting from the first excited state for different values of the screening parameter.
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.
Abstract: In this study, the Schrödinger equation was solved with a superposition of the Hulthen potential and generalized inverse quadratic Yukawa potential model using the Nikiforov-Uvarov (NU) method. For completeness, we also calculated the wave function. To validate our results, the numerical bound state energy eigenvalues was computed for various principal n and angular momentum l quantum numbers. With the aid of the Hellmann-Feynman theorem, the expressions for the expectation values of the square of inverse of position, r^(-2), inverse of position, r^(-1), kinetic energy, T ̂ and square of momentum, p ̂ are calculated. By adjusting the potential parameters, special cases of the potential were considered, resulting in Generalized Inverse Quadratic Yukawa potential, Hulthen potential, Coulomb potential, Kratzer potential, Inversely Quadratic Yukawa potential and Coulomb plus inverse square potential, respectively. Their energy eigenvalue expressions and numerical computations agreed with the literature. Keywords: Schrödinger equation, Hulthen potential (HP), Generalized inverse quadratic Yukawa potential (GIQYP), Nikiforov-Uvarov method. PACS: 03.65.−w, 03.65.Ca, 03.65.Ge.
In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.
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.
The Schrödinger equation was solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov–Uvarov – functional analysis (NUFA) method. The bound-state energy and wave function for the HSKP were obtained in a closed form by applying the Greene–Aldrich approximation scheme to the inverse-square term. Using the resulting energy equation, we computed the energy spectra for 12 diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H2, ScH, CO, I2, N2, and NO) for various quantum states. To show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.