Analysis of the Dirac equation with the Killingbeck potential in non-commutative space

In this paper, we investigate the Dirac equation with the Killingbeck potential under the external magnetic field in non-commutative space. Corresponding to the expressions of the energy level and wave functions in spin symmetry limit and pseudo-spin symmetry limit are derived by using the Bethe ansatz method. The parameter B associated with the external magnetic field and non-commutative parameter {\theta} make to modify the energy level for considered systems.