Quantum Theory of Continuous Observations Some Significant Examples

  • Giovanni Maria Prosperi
Part of the International Centre for Mechanical Sciences book series (CISM, volume 294)


Ordinary Quantum Mechanics has to do with an idealized situation in which a system is prepared in a given state at an initial time t 0 , it is left to evolve freely for some time and it is submitted to some kind of measurement at a single final time t 1 or at certain well separated subsequent times t 1 , t 2,... In any case the single process is considered as pratically istantaneous.


Quantum Theory Continuous Observation Poissonian Case Ordinary Quantum Mechanics Dimensional Complex Space 
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  1. 1).
    E.B. Davies, Quantum theory of open systems. (Academic London, 1976).MATHGoogle Scholar
  2. 2).
    E.B. Davies, IEEE Trans. Inf. Theory 23 (1977), 530;CrossRefMATHGoogle Scholar
  3. 2a).
    M.D. Srinivas, J. Math. Phys. 18 (1977), 2138;ADSCrossRefMATHMathSciNetGoogle Scholar
  4. 2b).
    M.D. Srinivas and E.B. Davies, Opt. Acta 28 (1981), 981.ADSCrossRefMathSciNetGoogle Scholar
  5. 3).
    A. Barchielli, L. Lanz and G.M. Prosperi, Nuovo Cimento, 72 B (1982), 79; Found. of Physics, 13 (1983), 779.CrossRefMathSciNetGoogle Scholar
  6. 4).
    G. Lupieri, J. Math. Phys. 24 (1983), 2329.ADSCrossRefMATHMathSciNetGoogle Scholar
  7. 5).
    A. Barchielli, Nuovo Cimento, 74 B (1983), 113; Phys. Rev. D 32 (1985), 347; preprint IFUM 311/FT (1985).CrossRefMathSciNetGoogle Scholar
  8. 6).
    A. Barchielli and G. Lupieri, J. Math. Phys. 26 (1985), 2222; Lect. Notes in Math. 1136 (Springer, Berlin, 1986), 57.ADSCrossRefMATHMathSciNetGoogle Scholar
  9. 7).
    L. Lanz, O. Melsheimer and S. Penati, preprint Univ. di Milano 1985.Google Scholar
  10. 8).
    Revue papers: G.M. Prosperi, Lect. Notes in Math. 1055 (Springer, Berlin, 1984), 301; A. Barchielli, L. Lanz and G.M. Prosperi, Proc. I.S.Q.M. Tokyo 1984, 165; Proc. Chaotic Behaviour in Q.S. Como 1984 (Plenum, New York, 1985), 321.Google Scholar
  11. 9).
    A. Rimini, Proc. Theoretical Physics Meeting — Amalfi, (ESI, Napoli, 1984), 275. G.C. Ghirardi, A. Rimini and T. Weber, I.C.T.P. preprint, IC/85/292.Google Scholar
  12. 10).
    Prof. V.P. Belavkin has kindly comunicated me that continuous observation can be treated even in the context of his formalism on control theory. (Cf. this volume).Google Scholar
  13. 11).
    K. Kraus, States, Effects, and Operations, Lect. Notes in Phys., 190 (Springer, Berlin, 1983); G. Ludwig, Foundations of Quantum Mechanics (Springer, Berlin, 1982); A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North Holland, Amsterdam, 1982); E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime (Reidel, Pordrecht and Boston, 1983).MATHGoogle Scholar
  14. 12).
    I.M. Gel’fand and N. Ya Vilenkin, Generalized Functions, Application of Harmonic Analysis, vol. 4 (Academic New York and London, 1964); M.C. Reed, Lect. Notes in Phys. 25 (Springer, Berlin, 1973).Google Scholar
  15. 13).
    V. Gorini, A. Kossakorowki and E.C.G. Sudarshan, J. Math., Phys. 17 (1976), 821.ADSCrossRefGoogle Scholar
  16. 14).
    G. Lidblad, Comm. Math. Phys. 48 (1976), 119.ADSCrossRefMathSciNetGoogle Scholar
  17. 15).
    R.L. Hudson and K.R. Parthasarathy, Comm. Math. Phys. 93 (1984), 301;ADSCrossRefMATHMathSciNetGoogle Scholar
  18. 15a).
    R.L. Hudson and K.R. Parthasarathy, Acta Appl. Math. 2 (1984), 353.CrossRefMATHMathSciNetGoogle Scholar
  19. 16).
    K.R. Parthasarathy, preprint Indian Statistical Inst., New Delhi 1985.Google Scholar
  20. 17).
    A.S. Holevo, preprint Steklov Math. Inst. Moskow, 1986.Google Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • Giovanni Maria Prosperi
    • 1
  1. 1.University of MilanMilanItaly

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