逆量子统计的贝叶斯方法：量子理论的Feynman路径积分表示中势的重构
Bayesian Approach to Inverse Quantum Statistics: Reconstruction of Potentials in the Feynman Path Integral Representation of Quantum Theory
摘要：
量子理论的费曼路径积分表示被用于非参数贝叶斯方法中，以从正则系综上的测量确定量子势。这种表示允许研究明确的经典和半经典的限制，并提供了一个统一的描述功能积分：费曼路径积分的统计算子，并在空间的潜力计算预测密度的积分。后者被视为最大后验近似，和各种近似计划，前者的开发和讨论。一个简单的数值例子说明了该方法的适用性。
英文摘要：
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator, and the integration over the space of potentials for calculating the predictive density. The latter is treated in maximum a posteriori approximation, and various approximation schemes for the former are developed and discussed. A simple numerical example shows the applicability of the method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
