Investigation of spin-$0$ massive charged particle subject to a homogeneous magnetic field with potentials in a topologically trivial flat class of G\"{o}del-type space-time

In this paper, we investigate relativistic quantum dynamics of spin- $0$ massive charged particle subject to a homogeneous magnetic field in the G"{o}del-type space-time with potentials. We solve the Klein-Gordon equation subject to a homogeneous magnetic field in a topologically trivial flat class of G"{o}del-type space-time in the presence of a Cornell-type scalar and Coulomb-type vector potentials and analyze the effects on the energy eigenvalues and eigenfunctions.