Statistics of local value in quantum mechanics

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	Statistics of local value in quantum mechanics
	Luo, SL
	2002-09-01
发表期刊	INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
ISSN	0020-7748
卷号	41 期号:9 页码:1713-1731
摘要	Given 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.
关键词	local value classical observable Fisher information conditional expectation Heisenberg uncertainty principle
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000179181800006
出版者	KLUWER ACADEMIC/PLENUM PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17056
专题	应用数学研究所
通讯作者	Luo, SL
作者单位	1.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
推荐引用方式 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.