arXiv:quant-ph/0512160 · Physical Review A

Time-extended measurement of the position of a particle

Francesc S. Roig

Published Apr 18, 2006• 2 citations

Abstract

The von Neumann interaction between a particle and an apparatus has been considered in the measurement of the position of a particle when the interaction lasts for a finite amount of time. When the measurement has finite duration, both the motion of the pointer and the particle influences the result of the measurement. Provided that the particle is in an eigenstate of its position at the start of the measurement, the pointer will indicate the arithmetic average between the initial and final position of the particle. Furthermore, the probability that the pointer will indicate a given average value is equal to the transition probability for the undisturbed particle to experience the change in position. If the initial state of the pointer is a narrow wave packet, then for any initial state of the particle, the measurement yields, approximately, the undisturbed probability distribution for the position of the particle at the end of the measurement.

DOI: 10.1103/physreva.73.042106

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