 96403 Erdos L., Solovej J.P.
 Semiclassical eigenvalue estimates for the Pauli operator
with strong nonhomogeneous magnetic fields: I. Nonasymptotic
LiebThirring type estimate
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Sep 9, 96

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Abstract. We give the first LiebThirring 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 nonhomogeneous magnetic fields.
This enables us, in the companion paper \cite{ESII},
to obtain the leading order semiclassical eigenvalue asymptotic,
which, in turn, leads to the proof of the validity of the
magnetic ThomasFermi theory of \cite{LSYII}. Our
work generalizes the results of \cite{LSYII} to nonhomogeneous
magnetic fields.
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