Numerical Bootstrap in Quantum Mechanics

TL;DR

This paper evaluates the numerical bootstrap method's effectiveness in quantum mechanics, demonstrating its ability to accurately capture non-perturbative effects, supersymmetric spectra, and large N behaviors in various quantum systems.

Contribution

It applies and tests the numerical bootstrap technique in quantum mechanics, showing its accuracy in different potentials and models, including supersymmetric and large N systems.

Findings

Bootstrap captures non-perturbative effects in double well potential

Accurately reproduces spectra of supersymmetric quantum systems

Yields results consistent with saddle point analysis at large N

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.