96-403 Erdos L., Solovej J.P.

Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields: I. Non-asymptotic Lieb-Thirring type estimate (114K, LaTeX) Sep 9, 96

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Abstract. We give the first Lieb-Thirring type estimate on the sum of the negative eigenvalues of the Pauli operator that behaves as the corresponding semiclassical expression even in the case of strong non-homogeneous magnetic fields. This enables us, in the companion paper \cite{ES-II}, to obtain the leading order semiclassical eigenvalue asymptotic, which, in turn, leads to the proof of the validity of the magnetic Thomas-Fermi theory of \cite{LSY-II}. Our work generalizes the results of \cite{LSY-II} to non-homogeneous magnetic fields.

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