Quantum particle in a random potential: Exact solution and its implications

I accurately solve the Schr\"odinger equation in a magnetic field B in an arbitrary set of two-dimensional point potentials. When B=0, they yield a mobility edge. When B{≠}0, all states are localized below a certain energy Ec(B). Above Ec(B), they are extended at the Landau energies. At other energies the localization length is a discontinuous function of B at every rational value of eBd²/ch, where d is an average interpotential distance.