TY - JOUR

T1 - Schrödinger operators periodic in octants

AU - Korotyaev, Evgeny

AU - MØller, Jacob Schach

N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Eigenvalues

KW - Periodic Schrödinger operator

KW - Spectral bands

KW - dinger operator

KW - Periodic Schr&#246

UR - http://www.scopus.com/inward/record.url?scp=85104778209&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3466cf02-de50-3df5-9c4a-852662ddfccc/

U2 - 10.1007/s11005-021-01402-4

DO - 10.1007/s11005-021-01402-4

M3 - Article

AN - SCOPUS:85104778209

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

M1 - 55

ER -