# Bootstrapping Simple QM Systems

@inproceedings{Berenstein2021BootstrappingSQ, title={Bootstrapping Simple QM Systems}, author={David Berenstein and George Hulsey}, year={2021} }

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…

#### 5 Citations

Bootstrapping More QM Systems

- Physics
- 2021

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…

Comment on the Bootstrap Method in Harmonic Oscillator

- Physics
- 2021

We study the bootstrap method in harmonic oscillators in one-dimensional quantum mechanics. We find that the problem reduces to the Dirac’s ladder operator problem and is exactly solvable. Thus,…

Application of Bootstrap to $\theta$-term

- Physics
- 2021

Recently, novel numerical computation on quantum mechanics by using a bootstrap was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a θ-term, where the…

Bootstrapping Calabi-Yau Quantum Mechanics

- Physics
- 2021

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some…

Bootstrapping Lattice Vacua

- Physics
- 2021

This paper demonstrates the application of semidefinite programming to lattice field theories, showcasing spin chains and lattice scalar field theory. Requiring expectation values of manifestly…

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