Weak magnetic field solution of Schrödinger equation in two dimensions and continuous density of states

Green function method is applied to the solution of Schrödinger equation in two-dimensions where there is a constant and nearly uniform magnetic field Bo applied perpendicularly and there are infinitesimally weak scatterers within the system. Electronic density of states n(E) obtained from the average Green function go is a continuous function of energy E and not in the form of discrete Landau spikes even in the pure system with no disorder. Self consistent calculation of self-energy gives two possible scattering time values, one leading to resistance increase with Bo while the other causing decrease in resistance.