Spin-$0$ scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in $5D$ cosmic string space-time

In this paper, we study a relativistic quantum dynamics of spin-$0$ scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in the background of Kaluza-Klein theory (KKT). We solve Klein-Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov-Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the space-time, the scalar potential and the magnetic field which break their degeneracy.