Summary
The relation between the restricted path integral approach to quantum measurement theory and the commonly accepted von Neumann wave function collapse postulate is presented. It is argued that in the limit of impulsive measurements the two approaches lead to the same predictions. The example of repeated impulsive quantum measurements of position performed on a harmonic oscillator is discussed in detail and the quantum non-demolition strategies are recovered in both the approaches.
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References
von Neumann J. V.,Mathematische Grundlagen der Quantenmechanik (Springer, Berlin) 1932; English translation byBeyer R. T.,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton) 1955.
Mensky M. B.,Continuous Quantum Measurements and Path Integrals (IOP Publishers, Bristol and Philadelphia) 1993.
Feynman R. P. andHibbs H. R.,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, N.Y.) 1955.
Mensky M. B., Onofrio R. andPresilla C.,Phys. Lett. A,161 (1991) 236.
Mensky M. B., Onofrio R. andPresilla C.,Phys. Rev. Lett.,70 (1993) 2828.
Onofrio R., Presilla C. andTambini U.,Phys. Lett. A,183 (1993) 135;Tambini U., Presilla C. andOnofrio R.,Phys. Rev. A,51 (1995) 967.
Calarco T. andOnofrio R.,Macrorealism, non-invasivity and quantum mechanics: a quantitative approach, inProceedings of the Conference on Foundations of Quantum Mechanics, Lecce 1993 (Kluwer, Dordrecht) 1994;Phys. Lett. A,198 (1995) 279.
Caves C. V., Thorne K. S., Drever R. W., Sandberg V. andZimmermann M.,Rev. Mod. Phys.,52 (1980) 341.
Press W. H.,Numerical Recipes: the Art of Scientific Computing (Cambridge University Press, Cambridge) 1986.
Konetchnyi A., Mensky M. B. andNamiot V.,Phys. Lett. A,177 (1993) 283.
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Calarco, T. Impulsive quantum measurements: Restricted path integral vs. von Neumann collapse. Il Nuovo Cimento B 110, 1451–1461 (1995). https://doi.org/10.1007/BF02849843
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DOI: https://doi.org/10.1007/BF02849843