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Numerical Bootstrap in Quantum Mechanics

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arxiv 2108.11416 v2 pith:IBPNI2HA submitted 2021-08-25 hep-th quant-ph

Jyotirmoy Bhattacharya , Diptarka Das , Sayan Kumar Das , Ankit Kumar Jha , Moulindu Kundu This is my paper · ORCID
classification hep-thquant-ph
keywords bootstrapquantumfindmechanicalmechanicsmethodnumericalagree
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We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative aspects. Using this technique we then investigate quantum mechanical potentials related by supersymmetry and recover the expected spectra. Finally, we also study the singlet sector of O(N) vector model quantum mechanics, where we find that the bootstrap method yields results which in the large N agree with saddle point analysis.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stationarity is not enough: tightness of the quantum mechanical bootstrap and the copositive cone

    cs.SC 2026-08 accept novelty 8.0 of 10

    The stationary quantum bootstrap is provably not tight in two dimensions, while the eigenstate bootstrap appears to remain tight in the tested settings.

  2. Bootstrapping periodic quantum systems

    hep-th 2025-07 conditional novelty 7.0 of 10

    A bootstrap method that includes the translation operator and uses reality conditions computes accurate Bloch-band dispersion relations for the cosine potential without positivity constraints.

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