Bootstrapping More QM Systems
High Energy Physics - Theory
2022-06-29 v1 High Energy Physics - Lattice
Quantum Physics
Abstract
We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians. In this paper we focus on problems that have a two parameter search space in the bootstrap approach: the double well and a periodic potential associated to the Mathieu equation. For the double well, we compare the energies with contributions from perturbative and non-perturbative results, finding good agreement. For the periodic potentials, we notice that the bootstrap approach gives the band structure of the periodic potential, but it has trouble finding the quasi-momentum of the system. To make further progress on the dispersion relation of the bands, new techniques are needed.
Cite
@article{arxiv.2109.06251,
title = {Bootstrapping More QM Systems},
author = {David Berenstein and George Hulsey},
journal= {arXiv preprint arXiv:2109.06251},
year = {2022}
}