Spectral asymptotics for the Schrödinger operator with spreading and oscillating potentials

Vincent Duchêne (1, 2) , Nicolas Raymond (2)

1 CNRS - Centre National de la Recherche Scientifique
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 the oscillations, a reduction to a non-oscillating effective Hamiltonian is performed.

Domaines: Mathématiques [math]

Vincent Duchêne, Nicolas Raymond. Spectral asymptotics for the Schrödinger operator with spreading and oscillating potentials. 2016. ⟨hal-01361768v1⟩