• Corpus ID: 237213416

Bootstrapping Simple QM Systems

  title={Bootstrapping Simple QM Systems},
  author={David Berenstein and George Hulsey},
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… 

Figures from this paper

Bootstrapping More QM Systems
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
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
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
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
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
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


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