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Statistics of local value in quantum mechanics
Luo, SL
2002-09-01
Source PublicationINTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
ISSN0020-7748
Volume41Issue:9Pages:1713-1731
AbstractGiven a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie-Bohm's casual approach to quantum mechanics, instantaneous frequency in time frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and statistically. Furthermore, the current density in quantum mechanics, the osmotic velocity in stochastic mechanics, and the Fisher information in classical statistical inference, arise naturally in connection with local value. In particular, Heisenberg uncertainty principle can be quantified more precisely by virtue of local value.
Keywordlocal value classical observable Fisher information conditional expectation Heisenberg uncertainty principle
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000179181800006
PublisherKLUWER ACADEMIC/PLENUM PUBL
Citation statistics
Cited Times:22[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17056
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
2.City Univ Hong Kong, Liu Bie Ju Ctr Math Sci, Kowloon, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Luo, SL. Statistics of local value in quantum mechanics[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,2002,41(9):1713-1731.
APA Luo, SL.(2002).Statistics of local value in quantum mechanics.INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,41(9),1713-1731.
MLA Luo, SL."Statistics of local value in quantum mechanics".INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 41.9(2002):1713-1731.
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