On spectral estimates for two-dimensional Schrodinger operators
File(s)
Published version
Author(s)
Laptev, A
Solomyak, M
Type
Journal Article
Abstract
For the two-dimensional Schrödinger operator HαV=−Δ−αV, V≥0HαV=−Δ−αV, V≥0, we study the behavior of the number N−(HαV)N−(HαV) of its negative eigenvalues (bound states), as the coupling parameter αα tends to infinity. A wide class of potentials is described, for which N−(HαV)N−(HαV) has the semi-classical behavior, i.e. N−(HαV)=O(α)N−(HαV)=O(α). For the potentials from this class, the necessary and sufficient condition is found for the validity of the Weyl asymptotic law.
Date Issued
2013-01-01
Date Acceptance
2013-01-01
Citation
Journal of Spectral Theory, 2013, 3 (4), pp.505-515
ISSN
1664-0403
Publisher
European Mathematical Society
Start Page
505
End Page
515
Journal / Book Title
Journal of Spectral Theory
Volume
3
Issue
4
Copyright Statement
© 2016 EMS Publishing House. All rights reserved
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Schrodinger operator on R-2
bound states
spectral estimates
NEGATIVE SPECTRUM
Publication Status
Published