Consider a system of non-interacting particles with charge q and spin S confined to an area A = L x L y in the x-y plane. Apply a uniform magnetic field B = ( 0 0 B ) along the z -axis. In SI units, the Hamiltonian of this system (here, the effects of spin are neglected) is H ^ ^ = 1 2 m ( p ^ ^ − − q A ^ ^ ) 2 . Here, p ^ ^ is the canonical momentum operator and A ^ ^ is the operator for the electromagnetic vector potential A (in position space A ^ ^ = A ).