ON THE NUMBER OF NEGATIVE EIGENVALUES FOR A SCHRODINGER OPERATOR WITHMAGNETIC-FIELD

Authors
SHEN ZW
Citation
Zw. Shen, ON THE NUMBER OF NEGATIVE EIGENVALUES FOR A SCHRODINGER OPERATOR WITHMAGNETIC-FIELD, Communications in Mathematical Physics, 182(3), 1996, pp. 637-660
Citations number
19
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
182
Issue
3
Year of publication
1996
Pages
637 - 660
Database
ISI
SICI code
0010-3616(1996)182:3<637:OTNONE>2.0.ZU;2-Q
Abstract
We consider the Schrodinger operator with magnetic field [GRAPHICS] Un der certain conditions on the magnetic field B = curl a, we generalize the Fefferman-Phong estimates (Bull. A. M. S. 9, 129-206 (1983)) on t he number of negative eigenvalues for -Delta + V to the operator H. Up per and lower bounds are established. Our estimates incorporate the co ntribution from the magnetic field. The conditions on B in particular are satisfied if the magnetic potentials a(j)(x) are polynomials.