Abstract
The ground-state density of the Pauli operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in the large field limit, the naturally rescaled ground-state density function is bounded from above by the megnetic field, and under some additional conditions, the limit density function is equal to the magnetic field. A restatement of this result yields an estimate on the density of complex orthogonal polynomials with respect to a fairly general weight function. We also prove a special case of the paramagnetic inequality.
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Part of this research was conducted during the U.S.-Sweden Workshop on Spectral Methods sponsored by the NSF under grant INT-9217529. Partial support by NSF grant PHY90-19433 A02 is also acknowledged.