On the Number of Bound States for Schrödinger Operators with Operator-valued Potentials
نویسنده
چکیده
Cwikel’s bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel’s bound for the Lieb–Thirring constant L0,3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the dimension d ≥ 3) for the quotient L0,d/L cl 0,d, where L cl 0,d is the so-called classical constant. This gives some improvement in large dimensions.
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