Landau Hamiltonian: 

In dimension 2, consider the Schrödinger operator with constant magnetic




This result was first obtained by Combes - Hislop - K. under the additionnal
assumption:


Note that the IDS for the free Landau Hamiltonian is not Hölder continuous. 

One cannot apply Theorem 1 directly : the coefficients are not periodic.

But periodic w.r.t magnetic translations if the rational flux condition is satisfied.

In the case of irrational flux, one has to change the proof of the replacement of fact 1.