Abstract
In the case of multiple measurements we have found that there is nonzero decay width Γ (Δ) (even for bound states) and that, for relatively long time intervals Δ separating successive measurements, Γ (Δ) tends like Δ−k (k ≥ 1 according to the investigated model) to the asymptotic value Γo for unstable states and to zero for bound states. We have shown that the detector efficiencyZ ≠ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.
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References
M.A. Braun and K. Urbanowski,Found. of Physics 22,617 (1992).
E. g., J. M. Jauch,Foundations of Quantum Mechanics (Adisson-Wesley, Reding 1968).
K. Urbanowski, “Strange properties of short time evolution of the projection of a state vector”, preprint No WSP-IF 90-14, Pedagogical University, Zielona Gora 1990, to be published. K. Urbanowski,Europhys. Lett. 18, 291(1992).
E. g., A.J. Akhiezer and V.B. Bierestecki,Quantum Electrodynamic (in Russian) (Nauka, Moscow, 1981).
E. g., I.S. Gradshteyn and I.S. Ryzhik,Table of Integrals, Series and Products (Academic, New York, 1980).
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Braun, M.A., Urbanowski, K. On the decay width of multiply measured unstable state. Found Phys Lett 6, 481–490 (1993). https://doi.org/10.1007/BF00682795
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DOI: https://doi.org/10.1007/BF00682795