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Semiclassical spectral invariants for schr¨odinger operators

Victor Guillemin Massachusetts Institute of Technology Zuoqin Wang University of Michigan

Differential Geometry mathscidoc:1609.10266

Journal of Differential Geometry, 91, (1), 103-128, 2012
In this article we show how to compute the semiclassical spectral measure associated with the Schr¨odinger operator on Rn, and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schr¨odinger operator on R2 with a radially symmetric electric potential, V , and magnetic potential, B, both V and B are spectrally determined.) We also show that in one dimension there is a very simple explicit identity relating the spectral measure of the Schr¨odinger operator with its Birkhoff canonical form.
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@inproceedings{victor2012semiclassical,
  title={SEMICLASSICAL SPECTRAL INVARIANTS FOR SCHR¨ODINGER OPERATORS},
  author={Victor Guillemin, and Zuoqin Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913225722905225928},
  booktitle={Journal of Differential Geometry},
  volume={91},
  number={1},
  pages={103-128},
  year={2012},
}
Victor Guillemin, and Zuoqin Wang. SEMICLASSICAL SPECTRAL INVARIANTS FOR SCHR¨ODINGER OPERATORS. 2012. Vol. 91. In Journal of Differential Geometry. pp.103-128. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913225722905225928.
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