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}
}