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Physica Scripta

Relativistic solutions for double ring-shaped oscillator potential via asymptotic iteration method

F. Yasuk, Ayşen Durmuş

Published Dec 13, 2007• 33 citations
Publisher

Abstract

The three dimensional Klein–Gordon equation is solved with a double ring-shaped oscillator for the case of the equal vector and scalar potential, , by using the asymptotic iteration method which is very efficient, systematic and practical. The bound states energy eigenvalues and corresponding eigenfunctions are presented for a particle bound in a potential of a double ring-shaped oscillator.

DOI
10.1088/0031-8949/77/01/015005

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The three dimensional Klein–Gordon equation is solved with a double ring-shaped oscillator for the case of the equal vector and scalar potential, , by using the asymptotic iteration method which is very efficient, systematic and practical. The bound states energy eigenvalues and corresponding eigenfunctions are presented for a particle bound in a potential of a double ring-shaped oscillator.
In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. 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.