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.
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Communicated by Christian Gérard.
Dedicated to the memory of B.M. Levitan
Submitted: September 5, 2007. Accepted: November 12, 2007.
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Parnovski, L. Bethe–Sommerfeld Conjecture. Ann. Henri Poincaré 9, 457–508 (2008). https://doi.org/10.1007/s00023-008-0364-x
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DOI: https://doi.org/10.1007/s00023-008-0364-x