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Annales Henri Poincaré

, Volume 9, Issue 3, pp 457–508 | Cite as

Bethe–Sommerfeld Conjecture

  • Leonid ParnovskiEmail author
Article

Abstract.

We consider Schrödinger operator −Δ + V in \({\mathbb{R}}^d (d \geq 2)\) with smooth periodic potential V and prove that there are only finitely many gaps in its spectrum.

Keywords

Asymptotic Formula Conjugate Point Integer Vector Operator Pencil Compact Resolvent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUnited Kingdom

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