Position Uncertainty in the Heisenberg Uncertainty Relation
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Publication:3566529
DOI10.1143/PTP.123.431zbMATH Open1189.81120arXiv1002.3005MaRDI QIDQ3566529
Publication date: 8 June 2010
Published in: Progress of Theoretical Physics (Search for Journal in Brave)
Abstract: Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg uncertainty relation between the position uncertainty and momentum disturbance holds when the measurement error epsilon(x_t) for the object position x_t is adopted as the position uncertainty. However, the uncertainty in the measurement result obtained for x_0 is the standard deviation of the measurement result, and not the measurement error epsilon(x_0). This difference is due to the reduction of a wave packet. The validity of the linearity assumption is examined in detail.
Full work available at URL: https://arxiv.org/abs/1002.3005
Quantum measurement theory, state operations, state preparations (81P15) Commutation relations and statistics as related to quantum mechanics (general) (81S05)
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