论文标题
假人的光谱定理：关于量子概率和随机变量理论的教学讨论
Spectral theorem for dummies: A pedagogical discussion on quantum probability and random variable theory
论文作者
论文摘要
约翰·冯·诺伊曼（John von Neumann）的自偶会操作员的光谱定理是量子力学的基石。除其他事项外，它还提供了自相邻操作员的期望值与实现的随机变量的期望值之间的联系。本文以Dirac的胸罩和KET符号为基础，基于物理直觉，对该定理进行了简单的口语表述，并提供了对执行实际计算很重要的技术。目的是让学生对经典和量子力学中随机变量的使用中的相似性和差异进行建设性讨论。特别强调的是运算符，这些操作员是非互动自动化运营商的简单功能。演示文稿是独立的，包括最相关结果的详细计算。
John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint operators and expected values of real-valued random variables. This paper presents a plain-spoken formulation of this theorem in terms of Dirac's bra and ket notation, which is based on physical intuition and provides techniques that are important for performing actual calculations. The goal is to engage students in a constructive discussion about similarities and differences in the use of random variables in classical and quantum mechanics. Special emphasis is given on operators that are simple functions of noncommuting self-adjoint operators. The presentation is self-contained and includes detailed calculations for the most relevant results.
