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On the number of bound states for Schrödinger operators with operator-valued potentials

Dirk Hundertmark Department of Mathematics 253-37, California Institute of Technology

TBD mathscidoc:1701.332975

Arkiv for Matematik, 40, (1), 73-87, 2000.11
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$L$_{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$d$≥3) for the quotient$L$_{0,d}/L^{cl}_{0,d}is the so-called classical constant. This gives some improvement in large dimensions.
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@inproceedings{dirk2000on,
  title={On the number of bound states for Schrödinger operators with operator-valued potentials},
  author={Dirk Hundertmark},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603727693784},
  booktitle={Arkiv for Matematik},
  volume={40},
  number={1},
  pages={73-87},
  year={2000},
}
Dirk Hundertmark. On the number of bound states for Schrödinger operators with operator-valued potentials. 2000. Vol. 40. In Arkiv for Matematik. pp.73-87. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603727693784.
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