Bootstrapping Simple QM Systems
High Energy Physics - Theory
2021-09-17 v2 High Energy Physics - Lattice
Quantum Physics
Abstract
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 potentials converge exponentially fast.
Keywords
Cite
@article{arxiv.2108.08757,
title = {Bootstrapping Simple QM Systems},
author = {David Berenstein and George Hulsey},
journal= {arXiv preprint arXiv:2108.08757},
year = {2021}
}
Comments
14 pages, 9 figures. v2: minor changes, references added