The uncertainty relation between energy and time of measurementстатья

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[1] Vorontsov Y. I. The uncertainty relation between energy and time of measurement // Sov. Phys. Uspekhi. — 1981. — Vol. 24. — P. 150–158. Contrary to a wide-spread impression, the possibility of measuring an energy in a finite time without changing its initial value (E' =E0) is not in contradiction with the principles of quantum mechanics. The relation Δ(E'-E0)Δt≥ 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 H1, of the system and the apparatus depend on the energy operator Ê and that the operators Ĥ and Ê commute. It is also possible to have a nonperturbing measurement in which the error in measuring the energy is so small that ΔE/Δt. Measurement of the energy of a given system is accompanied by an increase in the uncertainty Δε of the energy of the apparatus. The error ΔE in the measurement of the system's energy and the perturbation Δεof the energy of the apparatus are connected by the relations (ΔE + Δε) centerdot Δt≥ and ΔE centerdot Δε≥(/2Δt)2. [ DOI ]

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