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 is tightly confined in the z direction. Then, a magnetic field is applied in the z direction and according to the Landau gauge the electromagnetic vector potential is A = ( 0 , B x , 0 ) and the scalar potential is ϕ ϕ = 0 . Thus the Schrödinger equation for a particle of charge q and effective mass m ∗ ∗ in this system is: