Analytic l-state solutions of the kleingordon equation for q-deformed woodssaxon plus generalized ring shape potential for the two cases of equal and different mixed vector and scalar potentials

摘要

The analytical expressions for the eigenvalues and eigenvectors of the KleinGordon equation for q-deformed WoodsSaxon plus new generalized ring shape potential are derived within the asymptotic iteration method in two cases, namely, the case of equal mixed vector and scalar potentials and the case when the vector potential is chosen to be equal to the q-deformed WoodsSaxon plus the new generalized ring-shaped potential while the scalar one is taken equal to the ring-shaped potential. The latter is considered as a small perturbation. The obtained eigenvalues are given in a closed form and the corresponding normalized eigenvectors, for any l, are formulated in terms of the generalized Jacobi polynomials for the radial part of the KleinGordon equation and associated Legendre polynomials for its angular one. When the shape deformation is canceled, we recover the same solutions previously obtained by the NikiforovUvarov method for the standard spherical WoodsSaxon potential. It is also shown that, from the obtained results, we can derive the solutions of this problem for Hulthen potential.