Abstract
We consider the Schrödinger operator with magnetic field H = ∑nj=1 (1/i ∂/∂xj - aj)2 + V in ℝn. Under certain conditions on the magnetic field B = curl a, we generalize the Fefferman-Phong estimates (Bull. A. M. S. 9, 129-206 (1983)) on the number of negative eigenvalues for -Δ + V to the operator H. Upper and lower bounds are established. Our estimates incorporate the contribution from the magnetic field. The conditions on B in particular are satisfied if the magnetic potentials aj(x) are polynomials.
Original language | English |
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Pages (from-to) | 637-660 |
Number of pages | 24 |
Journal | Communications in Mathematical Physics |
Volume | 182 |
Issue number | 3 |
DOIs | |
State | Published - 1996 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics