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An Estimate of the Gap of the First Two Eigenvalues in the Schr\" odinger Operator

Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43579

arXiv preprint arXiv:0902.2250, 1985.2
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the potential is bounded from below by a positive constant, the gap has a lower bound independent of the dimension. We also estimate the gap when the potential is not necessarily convex.
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@inproceedings{shing-tung1985an,
  title={An Estimate of the Gap of the First Two Eigenvalues in the Schr\" odinger Operator},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204207689593143},
  booktitle={arXiv preprint arXiv:0902.2250},
  year={1985},
}
Shing-Tung Yau. An Estimate of the Gap of the First Two Eigenvalues in the Schr\" odinger Operator. 1985. In arXiv preprint arXiv:0902.2250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204207689593143.
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