Approximate bound state solutions of the Klein-Gordon equation with the linear combination of Hulthén and Yukawa potentials

Publication date: Available online 2 July 2019Source: Physics Letters AAuthor(s): A.I. Ahmadov, S.M. Aslanova, M.Sh. Orujova, S.V. Badalov, Shi-Hai DongAbstractBased on a developed scheme we show how to deal with the centrifugal term and the Coulombic behavior part and then to solve the Klein-Gordon (KG) equation for the linear combination of Hulthén and Yukawa potentials. Two cases, i.e., the scalar potential which is equal and unequal to vector potential, are considered for arbitrary l state. With the aid of the Nikiforov-Uvarov (NU) method and the traditional approach, we present the eigenvalues and the corresponding radial wave functions expressed by the Jacobi polynomials or hypergeometric functions and find that the results obtained by them are consistent. For given values of potential parameters V0,V0′,S0,S0′ and M=1, we notice that the energy levels E are sensitively relevant for the potential parameter δ and the energy levels E increase for δ>0.1 as quantum numbers nr and l increase. However, for δ∈(0,0.1) the energy levels E do not always increase with the quantum numbers nr and l. We find that the energy levels E are inversely proportional to quantum numbers nr and l when δ∈(0,0.05).

Source: Physics Letters A - July 3, 2019 Category: Physics Source Type: research