Issues

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1981

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February

  

Methodological notes


The uncertainty relation between energy and time of measurement


Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

Contrary to a wide-spread impression, the possibility of measuring an energy in a finite time without changing its initial value $(E'=E_0)$ is not in contradiction with the principles of quantum mechanics. The relation $\Delta(E'-E_0)\Delta t\ge\hslash$ holds only in the case when the energy of interaction between the quantum system in question and the apparatus is a function of a coordinate of the system. The condition for a nonperturbing energy measurement is that the interaction energy $H_1$, of the system and the apparatus depend on the energy operator $\hat E$ and that the operators $\hat H$ and $\hat E$ commute. It is also possible to have a nonperturbing measurement in which the error in measuring the energy is so small that $\Delta E\ll\hslash/\Delta t$. Measurement of the energy of a given system is accompanied by an increase in the uncertainty $\Delta\varepsilon$ of the energy of the apparatus. The error $\Delta E$ in the measurement of the system's energy and the perturbation $\Delta\varepsilon$ of the energy of the apparatus are connected by the relations $(\Delta E+\Delta\varepsilon)\cdot\Delta t\ge\hslash$ and $\Delta E\cdot\Delta\varepsilon)\ge(\hslash/2\Delta t)^2$.

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Fulltext is also available at DOI: 10.1070/PU1981v024n02ABEH004638
PACS: 03.65.Bz
DOI: 10.1070/PU1981v024n02ABEH004638
URL: https://ufn.ru/en/articles/1981/2/e/
Citation: Vorontsov Yu I "The uncertainty relation between energy and time of measurement" Sov. Phys. Usp. 24 150–158 (1981)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks
@article{Vorontsov:1981,
	author = {Yu. I. Vorontsov},
	title = {The uncertainty relation between energy and time of measurement},
	publisher = {Physics-Uspekhi},
	year = {1981},
	journal = {Phys. Usp.},
	volume = {24},
	number = {2},
	pages = {150-158},
	url = {https://ufn.ru/en/articles/1981/2/e/},
	doi = {10.1070/PU1981v024n02ABEH004638}
}

Оригинал: Воронцов Ю И «Соотношение неопределенности энергия — время измерения» УФН 133 351–365 (1981); DOI: 10.3367/UFNr.0133.198102f.0351

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