翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Born's law : ウィキペディア英語版
Born rule

The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results; for example, while it has been claimed that Born's law can be derived from the Many Worlds Interpretation, the proofs have been criticized as circular.〔N.P. Landsman, ("The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle." ), in ''Compendium of Quantum Physics'' (eds.) F.Weinert, K. Hentschel, D.Greenberger and B. Falkenburg (Springer, 2008), ISBN 3-540-70622-4〕 However, within the Quantum Bayesianism interpretation of quantum theory, it has been shown to be an extension of the standard Law of Total Probability, which takes into account the Hilbert space dimension of the physical system involved.〔(Fuchs, C. A. ''QBism: the Perimeter of Quantum Bayesianism'' 2010 )〕 The Born rule can however be derived in the ambit of so-called Hidden-Measurements Interpretation of quantum mechanics, by averaging over all possible measurement-interactions that can take place between the quantum entity and the measuring system.〔Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics, Journal of Mathematical Physics, 27, pp. 202-210.〕〔Aerts, D. and Sassoli de Bianchi, M. (2014). The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem. Annals of Physics 351, Pages 975–1025 ((Open Access )).〕
== The rule ==

The Born rule states that if an observable corresponding to a Hermitian operator
A
with discrete spectrum is measured in a system with normalized wave function
\scriptstyle|\psi\rang
(''see'' bra–ket notation), then
* the measured result will be one of the eigenvalues \lambda of A, and
* the probability of measuring a given eigenvalue \lambda_i will equal \scriptstyle\lang\psi|P_i|\psi\rang, where P_i is the projection onto the eigenspace of A corresponding to \lambda_i.
:(In the case where the eigenspace of A corresponding to \lambda_i is one-dimensional and spanned by the normalized eigenvector \scriptstyle|\lambda_i\rang, P_i is equal to \scriptstyle|\lambda_i\rang\lang\lambda_i|, so the probability \scriptstyle\lang\psi|P_i|\psi\rang is equal to \scriptstyle\lang\psi|\lambda_i\rang\lang\lambda_i|\psi\rang. Since the complex number \scriptstyle\lang\lambda_i|\psi\rang is known as the ''probability amplitude'' that the state vector \scriptstyle|\psi\rang assigns to the eigenvector \scriptstyle|\lambda_i\rang, it is common to describe the Born rule as telling us that probability is equal to the amplitude-squared (really the amplitude times its own complex conjugate). Equivalently, the probability can be written as \scriptstyle|\lang\lambda_i|\psi\rang|^2.)
In the case where the spectrum of A is not wholly discrete, the spectral theorem proves the existence of a certain projection-valued measure Q, the spectral measure of A. In this case,
* the probability that the result of the measurement lies in a measurable set M will be given by \scriptstyle\lang\psi|Q(M)|\psi\rang.
If we are given a wave function
\scriptstyle\psi
for a single structureless particle in position space,
this reduces to saying that the probability density function
p(x,y,z)
for a measurement of the position at time
t_0
will be given by
p(x,y,z)=\scriptstyle|\psi(x,y,z,t_0)|^2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Born rule」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.