English

Bethe-Sommerfeld Conjecture

Spectral Theory 2009-11-13 v1

Abstract

We consider Schroedinger operator Δ+V-\Delta+V in RdR^d (d2d\ge 2) with smooth periodic potential VV and prove that there are only finitely many gaps in its spectrum.

Keywords

Cite

@article{arxiv.0801.3096,
  title  = {Bethe-Sommerfeld Conjecture},
  author = {Leonid Parnovski},
  journal= {arXiv preprint arXiv:0801.3096},
  year   = {2009}
}

Comments

59 pages, 10 figures; to appear in Annales Henri Poincare

R2 v1 2026-06-21T10:04:41.571Z