Schrödinger operators periodic in octants

Evgeny Korotyaev*, Jacob Schach MØller

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

We consider Schrödinger operators with periodic potentials in the positive quadrant on the plane with Dirichlet boundary conditions. We show that for any integer N and any interval I there exists a periodic potential such that the Schrödinger operator has N eigenvalues counted with multiplicity in this interval and there is no other spectrum in the interval. Furthermore, to the right and to the left of it there is a essential spectrum. Moreover, we prove similar results for Schrödinger operators for a product of an orthant and Euclidean space. The proof is based on the inverse spectral theory for Hill operators on the real line.

Original languageEnglish
Article number55
JournalLetters in Mathematical Physics
Volume111
Issue2
ISSN0377-9017
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Eigenvalues
  • Periodic Schrödinger operator
  • Spectral bands

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