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Probability Bracket Notation: the Unified Expressions of Conditional Expectation and Conditional Probability in Quantum Modeling
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Xing M. |
| Copyright Year | 2009 |
| Abstract | page 1 1. Introduction to PBN, indicator operator and CDO Abstract 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/0911.1462v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
