Quantum Bootstrap in Microcanonical Ensembles: Computational Insights and Applications

This paper explores the quantum bootstrap method, a promising numerical approach rooted in self-consistency conditions, and its application in microcanonical ensembles. Initially developed in the 1960s and ’70s, the bootstrap technique has found applications in various fields, including quantum mechanics, lattice theory, conformal field theory, and matrix models. While extensively studied in quantum mechanics, this paper introduces a classical correspondence to the quantum bootstrap method, expanding its applicability to microcanonical ensembles. The study incorporates a novel approach, demonstrating stronger constraints by integrating additional information in phase space. Numerical examples, including the double well potential, harmonic oscillator, Coulomb potential, and non-relativistic Toda model, illustrate the method’s effectiveness in resolving unphysical energy regions and improving computational precision. These results highlight its potential as a powerful tool in computational physics and quantum computing.