论文标题
部分可观测时空混沌系统的无模型预测
Different Bootstrap Matrices in Many QM Systems
论文作者
论文摘要
Bootstrap是一种最近开发的技术，旨在获得结合状态和相关函数的能量特征值。有三个关键步骤 - 递归方程，阳性约束，搜索空间。我们计算许多代表性量子力学系统的递归方程，例如多项式电位，指数势，Yukawa势和电磁电位。两种bootstrap矩阵与坐标与动量的坐标和耦合有关，并且显示了约束方程的能力。几乎是，我们分析了数值搜索中可能的问题，包括约束和步长的重要性，特征能水平和能量的变性。最后，我们尝试解释为什么引导程序通过分析谐波振荡器中创建操作员和an灭操作员的阳性约束来很好地工作。本文总结了自举量子力学（QM）的大多数知识，并显示了不同QM系统的特定引导方程和引导程序矩阵。
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations of many representative quantum mechanics systems, such as polynomial potential, exponential potential, Yukawa potential and electromagnetic potential. Two kinds of bootstrap matrices, which are about the coordinate and coupling of the coordinate with the momentum, and their ability of constraining equations are displayed. Nextly, we analyze possible questions in numerical search, including the importance of constraints and step length, eigen-energy level and the degeneracy of energy. Finally, we try to explain why the bootstrap work well by analyzing positivity constraints of creation operator and annihilation operator in harmonic oscillator. This article summarizes most knowledge of bootstrapping quantum mechanics (QM), and displays specific bootstrap equations and bootstrap matrices of different QM systems.
