On the number of negative eigenvalues for a Schrödinger operator with magnetic field

Zhongwei Shen

doi:10.1007/BF02506420

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

Zhongwei Shen

Producción científica: Article › revisión exhaustiva

8 Citas (Scopus)

Resumen

We consider the Schrödinger operator with magnetic field H = ∑ⁿ_j=1 (1/i ∂/∂xj - a_j)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 a_j(x) are polynomials.

Idioma original	English
Páginas (desde-hasta)	637-660
Número de páginas	24
Publicación	Communications in Mathematical Physics
Volumen	182
N.º	3
DOI	https://doi.org/10.1007/BF02506420
Estado	Published - 1996

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02506420

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abstract = "We consider the Schr{\"o}dinger 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.",

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PY - 1996

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N2 - 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.

AB - 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.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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ER -

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

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