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
UR - http://www.scopus.com/inward/record.url?scp=85104778209&partnerID=8YFLogxK
U2 - 10.1007/s11005-021-01402-4
DO - 10.1007/s11005-021-01402-4
M3 - Journal article
AN - SCOPUS:85104778209
SN - 0377-9017
VL - 111
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 2
M1 - 55
ER -