Bootstrapping Simple QM Systems

Abstract

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 potentials converge exponentially fast.

arXiv comment14 pages, 9 figures. v2: minor changes, references added

References in corpus (4)

• Supersymmetry and Quantum Mechanics
• Solving the 3D Ising Model with the Conformal Bootstrap
• Bootstrapping Matrix Quantum Mechanics
• Loop Equations and bootstrap methods in the lattice

Cited by in corpus (9)

• Numerical Bootstrap in Quantum Mechanics
• Bootstrapping More QM Systems
• Bootstrap bounds on D0-brane quantum mechanics
• Bootstrapping Calabi-Yau Quantum Mechanics
• Bootstrap Method in Harmonic Oscillator
• Application of Bootstrap to $\theta$-term
• From Noncommutative Geometry to Random Matrix Theory
• Bootstrap Method in Theoretical Physics
• Bootstrapping entanglement in quantum spin systems