On the Negative Spectrum of the Two-Dimensional Schrodinger Operator with Radial Potential
File(s)Laptev_Solomyak_final.pdf (350.93 KB)
Accepted version
Author(s)
Laptev, A
Solomyak, M
Type
Journal Article
Abstract
For a two-dimensional Schrödinger operatorHαV = −−αV with the radial
potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N−(HαV )
of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the
necessary and sufficient conditions for the semi-classical growth N−(HαV ) = O(α)
and for the validity of the Weyl asymptotic law.
potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N−(HαV )
of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the
necessary and sufficient conditions for the semi-classical growth N−(HαV ) = O(α)
and for the validity of the Weyl asymptotic law.
Date Issued
2012-08-01
Date Acceptance
2011-12-06
Citation
Communications in Mathematical Physics, 2012, 314 (1), pp.229-241
ISSN
1432-0916
Publisher
Springer Verlag (Germany)
Start Page
229
End Page
241
Journal / Book Title
Communications in Mathematical Physics
Volume
314
Issue
1
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-012-1501-4
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
2 SPATIAL DIMENSIONS
BOUND-STATES
Publication Status
Published