Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate
Erdös L, Solovej J. 1999. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. 96(1), 127–173.
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Journal Article
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Author
Erdös, LászlóISTA 
;
Solovej, Jan
;
Solovej, JanAbstract
We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. This result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier (1996). (orig.) 19 refs.
Publishing Year
Date Published
1999-01-15
Journal Title
Duke Mathematical Journal
Publisher
Duke University Press
Acknowledgement
The first author gratefully acknowledges financial support from the Eidgen6ssiche Technische Hochschule, Forschungsinstitut für Mathematik, Zürich, where this work was started. He is also grateful for the hospitality and support of Aarhus University during his visits there.
Volume
96
Issue
1
Page
127 - 173
ISSN
IST-REx-ID
Cite this
Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. 1999;96(1):127-173. doi:10.1215/S0012-7094-99-09604-7
Erdös, L., & Solovej, J. (1999). Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/S0012-7094-99-09604-7
Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” Duke Mathematical Journal. Duke University Press, 1999. https://doi.org/10.1215/S0012-7094-99-09604-7.
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate,” Duke Mathematical Journal, vol. 96, no. 1. Duke University Press, pp. 127–173, 1999.
Erdös L, Solovej J. 1999. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. 96(1), 127–173.
Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” Duke Mathematical Journal, vol. 96, no. 1, Duke University Press, 1999, pp. 127–73, doi:10.1215/S0012-7094-99-09604-7.
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