Question

How do energy eigenstates go between Landau levels?

Answer 1

Excited states move towards the edge, come down in energy, and then move away from the edge. In other words, there's a band crossing at the edge that allows states from the upper band to move to the lower band. This is similar to what happens in adiabatic charge pumping.

Answer 2

As a result, the charged particles can only occupy orbits with discrete energy values, called Landau levels. The Landau levels are degenerate, with the number of electrons per level directly proportional to the strength of the applied magnetic field.