Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. II: Leading order asymptotic estimates. (English) Zbl 0909.47052

Summary: 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. As in [E. H. Lieb, J. P. Solovej and J. Yngvason, Commun. Math. Phys. 161, 77-124 (1994; Zbl 0807.47058)] for homogeneous 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 in our companion paper [Part I, preprint 1996].


47N50 Applications of operator theory in the physical sciences
35P20 Asymptotic distributions of eigenvalues in context of PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory


Zbl 0807.47058
Full Text: DOI