Effects of the Kaluza–Klein theory on a Klein–Gordon particle with position-dependent mass

Abstract

Through the Kaluza–Klein theory, we investigate the quantum dynamics of a Klein–Gordon particle under the Aharonov–Bohm effect for bound states, where it is subject to the linear and Coulomb-type central potentials inserted in the Klein–Gordon equation by modification of the mass term. Then, we determine analytically solutions of bound states and the energy profile of the scalar particle in this background.