# 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…

## 6 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…

Bootstrapping Bloch bands

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single…

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…

## References

SHOWING 1-10 OF 17 REFERENCES

Numerical solution of lattice Schwinger-Dyson equations in the large-N limit

- Physics
- 1985

Abstract In this article, I establish the general leading large- N form of the Fokker-Planck operator for lattice gauge theories. In this formalism, the lattice Schwinger-Dyson equations appear…

Bootstrapping Dirac Ensembles

- Physics, Mathematics
- 2021

We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the…

Analytic and Numerical Bootstrap for One-Matrix Model and"Unsolvable"Two-Matrix Model

- Physics
- 2021

We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large N limit, developing and improving the recent proposal of H.Lin. It gives rigorous…

Solving the 3D Ising Model with the Conformal Bootstrap

- Physics
- 2012

We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars…

Loop Space Hamiltonians and Numerical Methods for Large $N$ Gauge Theories

- Physics
- 1983

Abstract We consider large- N gauge theories in the hamiltonian, collective field approach. We derive an alternative collective representation which leads to significant reduction when translation…

Loop Equations and bootstrap methods in the lattice

- Physics
- 2016

Abstract Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In…

Loop equation in Lattice gauge theories and bootstrap methods

- Mathematics
- 2018

In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for…

Supersymmetry and quantum mechanics

- Physics
- 1995

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why…

The Moment Problem

- Mathematics
- 2002

The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the…

Bootstrapping Matrix Quantum Mechanics.

- Physics, MedicinePhysical review letters
- 2020

It is shown that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology, where operator expectation values are related by symmetries and bounded with certain positivity constraints.