Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials
Vincent Duchêne, Nicolas Raymond · Documenta Mathematica · 2018
This study is devoted to the asymptotic spectral analysis of multiscale Schrödinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal form filtrating most of the oscillations, a reduction to a non-oscillating effective Hamiltonian is performed.