2009/11/07 by Xing Wang, Wang, Xing M.
Arts and Humanities · Physics and Astronomy · #81P16 #81Q99 #97K50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Philosophy and History of Science #Probability (math.PR) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.0911.1462
openalex publication_date 2009/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
After a brief introduction to Probability Bracket Notation (PBN), indicator operator and conditional density operator (CDO), we investigate probability spaces associated with various quantum systems: system with one observable (discrete or continuous), system with two commutative observables (independent or dependent) and a system of indistinguishable non-interacting many-particles. In each case, we derive unified expressions of conditional expectation (CE), conditional probability (CP), and absolute probability (AP): they have the same format for discrete or continuous spectrum; they are defined in both Hilbert space (using Dirac notation) and probability space (using PBN); and they may be useful to deal with CE of non-commutative observables.