The KG oscillator in the background of external magnetic field with a Cornell interaction in non-commutative quantum mechanics

In this paper, we investigated the two-dimensional Klein–Gordon 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 space, non-commutative space, and non-commutative space by using a quasi-exact methodology. The Hamiltonian was modified by the non-commutative parameter θ. We observed that the terms related to the deformation parameter can be taken as perturbation terms in QM. It was demonstrated that the non-commutative Hamiltonian was derived from the Moyal–Weyl multiplication and the Bopp shift method. We numerically calculated the energy spectrum in both commutative and non-commutative spaces. The behavior of all energies (the first, second, third, and fourth states) for the magnetic field was shown graphically. Furthermore, we derive the non-relativistic limit of the energy eigenvalues, which were comparable to the energy eigenvalues in the presence of the magnetic field in commutative space, known as the Zeeman effect.