Spectral asymptotics for the Schr\"odinger operator on the line with   spreading and oscillating potentials
  This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal form filtrating the oscillations, a reduction to a non-oscillating effective Hamiltonian is performed. 
Vincent Duch\^ene and Nicolas Raymond
math.SP