Corpus ID: 237213416

Bootstrapping Simple QM Systems

@inproceedings{Berenstein2021BootstrappingSQ,
  title={Bootstrapping Simple QM Systems},
  author={David Berenstein and George Hulsey},
  year={2021}
}
We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians, following the recent approach of Han, Hartnoll, and Kruthoff. We focus on comparing the bootstrap method data to known analytical predictions for the hydrogen atom and the harmonic oscillator. We resolve many energy levels for each, and more levels are resolved as the size of the matrices used to solve the problem increases. Using the bootstrap approach we find the spectrum of the Coulomb and harmonic… 

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TLDR
It is shown that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology, where operator expectation values are related by symmetries and bounded with certain positivity constraints.
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