English

Scattering and wave operators for one-dimensional Schr\"odinger operators with slowly decaying nonsmooth potentials

Spectral Theory 2007-05-23 v1 Mathematical Physics math.MP

Abstract

We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in Lp(R)L^p(\reals), p<2p<2. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We also prove asymptotic completeness of these wave operators for some classes of random potentials, and for almost every boundary condition for any given potential.

Keywords

Cite

@article{arxiv.math/0110140,
  title  = {Scattering and wave operators for one-dimensional Schr\"odinger operators with slowly decaying nonsmooth potentials},
  author = {M. Christ and A. Kiselev},
  journal= {arXiv preprint arXiv:math/0110140},
  year   = {2007}
}

Comments

46 pages

R2 v1 2026-07-22T16:40:53.163Z