96-404 Erdos L., Solovej J.P.

Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields: II. Leading order asymptotic estimates (175K, LaTeX) Sep 9, 96

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Abstract. 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 \cite{LSY-II} 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 \cite{ES-I}.

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