Annales Henri Poincaré

, Volume 9, Issue 3, pp 457–508

Bethe–Sommerfeld Conjecture


DOI: 10.1007/s00023-008-0364-x

Cite this article as:
Parnovski, L. Ann. Henri Poincaré (2008) 9: 457. doi:10.1007/s00023-008-0364-x


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.

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© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUnited Kingdom

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