 Since the system is subjected to a magnetic field, it has to be introduced as an electromagnetic vector potential in the Schrödinger equation.The system considered is an electron gas that is free to move in the x and y directions, but tightly confined in the z direction.Then, it is applied a magnetic field along the z direction and according to the Landau Gauge the electromagnetic vector potential is formula_2 and the scalar potential is formula_3.Thus the Schrödinger equation for a particle of charge formula_4 and effective mass formula_5 in this system is