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Ukrainian Journal of Physics

Interaction of Spinless Particles with Yukawa Ring-Shaped Potential

Akaninyene Daniel Antia, Eno E. Ituen, U.S. Jim, Effiong Ekpenyong Eyibio

Published Dec 13, 2017• 0 citations
Publisher

Abstract

We have obtained the approximate solutions of the Klein–Gordon equation with the Yukawa ring-shaped potential, by using the Nikiforov–Uvarov method for a special case of equal scalar and vector potentials. The energy eigenvalues for bound states and the corresponding wave functions are also obtained in a proper approximation. We have also shown that the results can be used to evaluate the energy eigenvalues of the Yukawa, angle-dependent, and Coulomb potentials. The numerical results are discussed and presented in the table and in the figure, which suggest their applicability to other systems. With the adjusted potential parameters given in the table, it is shown that the interaction of spinless (Klein–Gordon) particles with the Yukawa ring-shaped potential gives positive energy eigenvalues for the various quantum states.

DOI
10.15407/ujpe62.10.0913

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We have obtained the approximate solutions of the Klein–Gordon equation with the Yukawa ring-shaped potential, by using the Nikiforov–Uvarov method for a special case of equal scalar and vector potentials. The energy eigenvalues for bound states and the corresponding wave functions are also obtained in a proper approximation. We have also shown that the results can be used to evaluate the energy eigenvalues of the Yukawa, angle-dependent, and Coulomb potentials. The numerical results are discussed and presented in the table and in the figure, which suggest their applicability to other systems. With the adjusted potential parameters given in the table, it is shown that the interaction of spinless (Klein–Gordon) particles with the Yukawa ring-shaped potential gives positive energy eigenvalues for the various quantum states.
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Abstract In this study, the bound state solutions of the Klein-Fock-Gordon equation are examined for the sum of Manning-Rosen and Yukawa potential by using a recent improved scheme to deal with the centrifugal term. For any l ≠ 0, the energy eigenvalues and corresponding radial wave functions are determined under the condition of equal scalar and vector potentials. In order to obtain bound state solutions, we use two different methods called supersymmetric quantum mechanics (SUSYQM) and Nikiforov-Uvarov (NU) methods. The identical expressions for the energy eigenvalues are obtained, and the expression of radial wave functions transformations to each other is revealed via both methods. For arbitrary l states, the energy levels and the corresponding normalized eigenfunctions are given in terms of the Jacobi polynomials. A closed form of the normalized wave function is also obtained. It is seen that the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.
Applying an appropriate approximation scheme to deal with the centrifugal term, pseudospin and spin symmetric solutions of the Dirac–Yukawa problem with tensor interaction are investigated based on supersymmetric quantum mechanics (SUSYQM) and shape invariance (SI) formalism. We show that the energy eigenvalues equation is simply obtained by using the methodology of SUSYQM and SI. The corresponding wave functions are obtained in terms of hypergeometric functions. Effects of tensor interaction on the bound states and eigenfunctions are also investigated numerically. Further, we compare our results with those given in the literature, which are obtained by using the Nikiforov–Uvarov and asymptotic iteration methods.