In this paper, we investigate the two-dimensional Klein-Gordon (KG) oscillator in non-commutative quantum mechanics (NCQM). We also studied the case of a spin-0 particle moving in a background magnetic field with the Cornell potential in commutative, non-commutative space and non-commutative space by using a quasi-exact methodology. The Hamiltonians are modified by the non-commutative parameter θ. We see that the terms related to the deformation parameter can be taken as perturbation terms in QM. We demonstrate that the non-commutative Hamiltonian is derived by the Moyal-Weyl multiplication and the Bopp shift method. We numerically calculate the energy spectrum in both a commutative and non-commutative spaces. The behavior of all energies (the first, second, third, and fourth states) for the magnetic field is shown graphically. Furthermore, we derive the non-relativistic limit of the energy eigenvalues, which are comparable as the energy eigenvalues in the presence of the magnetic field in commutative space, known as the Zeeman effect.
