Bootstrapping More QM Systems

• URL: http://arxiv.org/abs/2109.06251v1
• Date: Mon, 13 Sep 2021 18:40:17 GMT
• Title: Bootstrapping More QM Systems
• Abstract summary: We focus on problems that have a two parameter search space in the bootstrap approach. For the double well, we compare the energies with contributions from perturbative and non-perturbative results. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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