 0133 Dirk Hundertmark
 On the number of bound states for Schr\"odinger operators
with operatorvalued potentials
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Jan 22, 01

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Abstract. Cwikel's bound is extended to an operatorvalued setting.
One application of this result is a semiclassical bound for
the number of negative bound states for Schr\"odinger operators
with operatorvalued potentials.
We recover Cwikel's bound for the LiebThirring constant
$L_{0,3}$ which is far worse than the best available by Lieb
(for scalar potentials). However, it leads to a uniform bound
(in the dimension $d\ge 3$) for the quotient
$L_{0,d}/ L^{\text{cl}}_{0,d}$, where $L^{\text{cl}}_{0,d}$ is
the socalled classical constant. This gives some improvement
in large dimensions.
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