DOI

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.

Язык оригиналаанглийский
Номер статьи55
Число страниц23
ЖурналLetters in Mathematical Physics
Том111
Номер выпуска2
DOI
СостояниеОпубликовано - апр 2021

    Предметные области Scopus

  • Статистическая и нелинейная физика
  • Математическая физика

ID: 86154317