Numerical Bootstrap in Quantum Mechanics

Abstract

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.

V1: 14 pages, 8 figures, V2: 14 pages, 12 figures, new appendix (B) added, new references added, published version

References in corpus (3)

• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• Bootstrapping Simple QM Systems
• Large N Optimization for multi-matrix systems

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• Bootstrap Method in Harmonic Oscillator
• Bootstrapping PT symmetric Hamiltonians
• Application of Bootstrap to $\theta$-term
• Bootstrapping the Kronig-Penney Model
• Anomalous Bootstrap on the half line
• From Noncommutative Geometry to Random Matrix Theory