English

Spectral asymptotics for the Schr\"odinger operator on the line with spreading and oscillating potentials

Spectral Theory 2021-10-01 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1609.01990,
  title  = {Spectral asymptotics for the Schr\"odinger operator on the line with spreading and oscillating potentials},
  author = {Vincent Duchêne and Nicolas Raymond},
  journal= {arXiv preprint arXiv:1609.01990},
  year   = {2021}
}