Calogero type bounds in two dimensions
File(s)
Accepted version
Author(s)
LAPTEV, AR
READ, LARRY
SCHIMMER, LUKAS
Type
Journal Article
Abstract
For a Schrödinger operator on the plane R2 with electric potential V and an Aharonov–Bohm magnetic field, we obtain an upper bound on the number of its negative eigenvalues in terms of the L1(R2)-norm of V. Similar to Calogero’s bound in one dimension, the result is true under monotonicity assumptions on V. Our method of proof relies on a generalisation of Calogero’s bound to operator-valued potentials. We also establish a similar bound for the Schrödinger operator (without magnetic field) on the half-plane when a Dirichlet boundary condition is imposed and on the whole plane when restricted to antisymmetric functions.
Date Issued
2022-07-23
Date Acceptance
2022-06-27
Citation
Archive for Rational Mechanics and Analysis, 2022, 245
ISSN
0003-9527
Publisher
Springer
Journal / Book Title
Archive for Rational Mechanics and Analysis
Volume
245
Copyright Statement
© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer
Nature (2022)
Nature (2022)
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000829126500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Technology
Mathematics, Applied
Mechanics
Mathematics
NEGATIVE EIGENVALUES
SCHRODINGER OPERATOR
DISCRETE SPECTRUM
STATES
NUMBER
INEQUALITIES
Publication Status
Published