, Volume 9, Issue 3, pp 457-508

Bethe–Sommerfeld Conjecture

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.

Dedicated to the memory of B.M. Levitan
Communicated by Christian Gérard.
Submitted: September 5, 2007. Accepted: November 12, 2007.