Bootstrap Method in Harmonic Oscillator

Abstract

Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this question, we study the bootstrap method in harmonic oscillators. We find that the problem reduces to the Dirac's ladder operator problem and is exactly solvable analytically. Our result suggests that the bootstrap method may be regarded as a numerical version of the Dirac's approach and it may explain why it works in various systems.

12 pages, no figures, v2 bootstrap analysis in an anharmonic oscillator by using ladder operators added and an appendix on constructing bootstrap matrix in a general polynomial potential added

References in corpus (6)

• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• Numerical Bootstrap in Quantum Mechanics
• Bootstrapping More QM Systems
• Bootstrapping Bloch bands
• Application of Bootstrap to $\theta$-term
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• Bootstrapping Shape Invariance: Numerical Bootstrap as a Detector of Solvable Systems
• Bootstrap Method in Theoretical Physics
• Bootstrapping periodic quantum systems