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日本物理學會誌

D.J. Simms and N.M.J Woodhouse, Lectures on Geometric Quanization, Springer-Verlag, Berlin and New York, 1976, vi+166ページ, 24.5×16.5cm, 3,200円(Lecture Notes in Physics, Vol. 53)

不二洋 荒木

Published Sep 5, 1977• 13 citations
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Next article Measurement and Filtering of Quantum Diffusion IIV. P. BelavkinV. P. Belavkinhttps://doi.org/10.1137/1139026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1984 Google Scholar[2] John von Neumann, Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, 1955xii+445, N.Y. 16,654a Google Scholar[3] A. S. Holevo, Probability and Stochastic Aspects of Quantum Theory, Princeton University Press, Princeton, N.J., 1955 Google Scholar[4] B. Misra and , E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Mathematical Phys., 18 (1977), 756–763 10.1063/1.523304 55:5076 CrossrefGoogle Scholar[5] V. P. Belavkin, A stochastic calculus of quantum input-output processes and quantum nondemolition filteringCurrent problems in mathematics. Newest results, Vol. 36 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, 29–67, 187 91f:81074 Google Scholar[6] Viacheslav P. Belavkin, Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processesModeling and control of systems in engineering, quantum mechanics, economics and biosciences (Sophia-Antipolis, 1988), Lecture Notes in Control and Inform. Sci., Vol. 121, Springer, Berlin, 1989, 245–265 1 231 124 0683.93084 CrossrefGoogle Scholar[7] V. P. Belavkin, Optimal quantum filtering of Markov signals, Problemy upravleniya i teoriya inform., 7 (1978), 345–360, (In Russian.) 0397.94001 Google Scholar[8] V. P. Belavkin, A. Blaquiere, Nondemolition measurement and control in quantum dynamical systemsInformation complexity and control in quantum physics (Udine, 1985), CISM Courses and Lectures, Vol. 294, Springer, Vienna, 1987, 311–329 913 955 CrossrefGoogle Scholar[9] V. P. Belavkin, B. 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Newest achievements, 36 (1989), 3–28 Google Scholar[14] V. P. Belavkin, Quantum continual measurements and a posteriori collapse on CCR, Comm. Math. Phys., 146 (1992), 611–635 93j:81006 0757.60057 CrossrefGoogle Scholar[15] V. P. Belavkin, A posterior Schrödinger equation for continuous nondemolition measurement, J. Math. Phys., 31 (1990), 2930–2934 10.1063/1.528946 91m:81020 0718.47035 CrossrefGoogle Scholar[16] V. P. Belavkin and , P. Staszewski, Nondemolition observation of a free quantum particle, Phys. Rev., Ser. A, 45 (1992), 1347–1356 10.1103/PhysRevA.45.1347 CrossrefGoogle Scholar[17] M. P. Evans and , R. L. Hudson, Multidimensional quantum diffusionsQuantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., Vol. 1303, Springer, Berlin, 1988, 69–88 91a:46065 0648.46056 CrossrefGoogle Scholar[18] R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394, Berlin 57:14125 R. S. Liptser and , A. N. 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Next article Measurement and Filtering of Quantum Diffusion IIV. P. BelavkinV. P. Belavkinhttps://doi.org/10.1137/1139026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York, 1984 Google Scholar[2] John von Neumann, Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, 1955xii+445, N.Y. 16,654a Google Scholar[3] A. S. Holevo, Probability and Stochastic Aspects of Quantum Theory, Princeton University Press, Princeton, N.J., 1955 Google Scholar[4] B. Misra and , E. C. G. Sudarshan, The Zeno's paradox in quantum theory, J. Mathematical Phys., 18 (1977), 756–763 10.1063/1.523304 55:5076 CrossrefGoogle Scholar[5] V. P. Belavkin, A stochastic calculus of quantum input-output processes and quantum nondemolition filteringCurrent problems in mathematics. Newest results, Vol. 36 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, 29–67, 187 91f:81074 Google Scholar[6] Viacheslav P. Belavkin, Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processesModeling and control of systems in engineering, quantum mechanics, economics and biosciences (Sophia-Antipolis, 1988), Lecture Notes in Control and Inform. Sci., Vol. 121, Springer, Berlin, 1989, 245–265 1 231 124 0683.93084 CrossrefGoogle Scholar[7] V. P. Belavkin, Optimal quantum filtering of Markov signals, Problemy upravleniya i teoriya inform., 7 (1978), 345–360, (In Russian.) 0397.94001 Google Scholar[8] V. P. Belavkin, A. Blaquiere, Nondemolition measurement and control in quantum dynamical systemsInformation complexity and control in quantum physics (Udine, 1985), CISM Courses and Lectures, Vol. 294, Springer, Vienna, 1987, 311–329 913 955 CrossrefGoogle Scholar[9] V. P. Belavkin, B. Grigelionis, Stochastic posterior equations for quantum nonlinear filteringProbability theory and mathematical statistics, Vol. I (Vilnius, 1989), “Mokslas”, Vilnius, 1990, 91–109, Proceedings of the Fifth Vilnius Conference 93b:81126 0914.60082 Google Scholar[10] V. P. Belavkin, A quantum nonadapted stochastic calculus and nonstationary evolution in Fock scaleQuantum probability & related topics, QP-PQ, VI, World Sci. Publishing, River Edge, NJ, 1991, 137–179 92m:81119 0937.60045 CrossrefGoogle Scholar[11] Viacheslav P. Belavkin, Quantum stochastic calculus and quantum nonlinear filtering, J. Multivariate Anal., 42 (1992), 171–201 10.1016/0047-259X(92)90042-E 93m:81013 0762.60059 CrossrefGoogle Scholar[12] R. L. Hudson and , K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys., 93 (1984), 301–323 86e:46057 0546.60058 CrossrefGoogle Scholar[13] A. S. Holevo, Quantum stochastic calculus, Itogi nauki tekhniki. Modern problems of mathematics series. Newest achievements, 36 (1989), 3–28 Google Scholar[14] V. P. Belavkin, Quantum continual measurements and a posteriori collapse on CCR, Comm. Math. Phys., 146 (1992), 611–635 93j:81006 0757.60057 CrossrefGoogle Scholar[15] V. P. Belavkin, A posterior Schrödinger equation for continuous nondemolition measurement, J. Math. Phys., 31 (1990), 2930–2934 10.1063/1.528946 91m:81020 0718.47035 CrossrefGoogle Scholar[16] V. P. Belavkin and , P. Staszewski, Nondemolition observation of a free quantum particle, Phys. Rev., Ser. A, 45 (1992), 1347–1356 10.1103/PhysRevA.45.1347 CrossrefGoogle Scholar[17] M. P. Evans and , R. L. Hudson, Multidimensional quantum diffusionsQuantum probability and applications, III (Oberwolfach, 1987), Lecture Notes in Math., Vol. 1303, Springer, Berlin, 1988, 69–88 91a:46065 0648.46056 CrossrefGoogle Scholar[18] R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394, Berlin 57:14125 R. S. Liptser and , A. N. Shiryayev, Statistics of random processes. II, Springer-Verlag, New York, 1978x+339, Berlin 58:7827 CrossrefGoogle Scholar[19] R. L. Stratonovitch, Conditional Markov Processes and their Application to Optimal Control Theory, Moscow State University, Moscow, 1966 Google Scholar[20] V. P. Belavkin, Chaotic states and stochastic integration in quantum systems, Russian Math. Surveys, 47 (1992), 47–106, (In Russian.) CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Open-system many-body dynamics through interferometric measurements and feedbackPhysical Review A, Vol. 94, No. 5 | 17 November 2016 Cross Ref Continuous Quantum Hypothesis TestingPhysical Review Letters, Vol. 108, No. 17 | 1 April 2012 Cross Ref Volume 39, Issue 3| 1995Theory of Probability & Its Applications History Submitted:08 October 1991Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1139026Article page range:pp. 363-378ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics