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.
|Number of pages||24|
|Journal||Communications in Mathematical Physics|
|State||Published - 1996|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics