Article

Annales Henri Poincaré

, Volume 9, Issue 3, pp 457-508

Bethe–Sommerfeld Conjecture

  • Leonid ParnovskiAffiliated withDepartment of Mathematics, University College London Email author 

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.