We investigated theoretically the magnetic field dependence of the quantum optical transition of qusi 2-Dimensional Landau splitting system, in GaN and ZnO. We apply the Quantum Transport theory (QTR) to the system in the confinement of electrons by square well confinement potential. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS). Through the analysis of this work, we found the increasing properties of the optical Quantum Transition Line Shapes(QTLSs) which show the absorption power and the Quantum Transition Line Widths(QTLWs) with the magnetic-field in GaN and ZnO. We also found that QTLW, ${gamma}(B)_{total}$ of GaN < ${gamma}(B)_{total}$ of ZnO in the magnetic field region B < 25 Tesla.