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Prog. Theor. Phys. Vol. 82 No. 4 (1989) pp. 665-681
Generalized Coherent State Approach to Quantum Measurement
Shoju Kudaka,
Shuichi Matsumoto,* and
Kiyotaka Kakazu
Department of Physics, University of the Ryukyus, Okinawa 903-01
*Department of Mathematics, University of the Ryukyus, Okinawa 903-01
(Received June 5, 1989)
Abstract:
We present and discuss some models for the quantum measuring process. Our models indicate that the coherent state approach to classical limits in quantum theories becomes a powerful method for a unified description of various measuring processes. Each detector in the models has a parameter N, the number of its dynamical variables; the whole process of an interaction between an object system and the detector is calculable for any finite number N. It is shown that the detector states after the interaction are characterized by a macroscopic parameter, which is closely connected with the “reliability” of the detector. The reliability plays an essential role in eliminating the quantum interference between two states corresponding to two different positions of the pointer. Finally, the quantum mechanics of the detector reduces to classical mechanics on suitable “phase space” as N becomes large, as is required.
URL :
http://ptp.ipap.jp/link?PTP/82/665/
DOI : 10.1143/PTP.82.665
References:
- See, for example,
J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer Verlag, Berlin, 1932).
D. Bohm, Quantum Theory (Prentice-Hall, Inc., New York, 1951).
A. Daneri, A. Loinger and G. M. Prosperi, Nucl. Phys. 33 (1962), 297[CrossRef].
H. Everett III, Rev. Mod. Phys. 29 (1957), 454[APS].
S. Machida and M. Namiki, Prog. Theor. Phys. 63 (1980), 1457[PTP]; ibid. 63 (1980), 1833[PTP].
H. Araki, Prog. Theor. Phys. 64 (1980), 719[PTP].
W. H. Zurek, Phys. Rev. D24 (1981), 1516[APS];
ibid. D26 (1982), 1862[APS].
M. Cini, Nuovo Cim. B73 (1983), 27.
D. F. Walls, M. J. Collet and G. J. Milburn, Phys. Rev. D32 (1985), 3208[APS].
R. Fukuda, Phys. Rev. A35 (1987), 8[APS];
ibid. A36 (1987), 3023[APS].
Z. Maki, Prog. Theor. Phys. 79 (1988), 313[PTP]; Soryushiron Kenkyu (Kyoto) 78 (1989), 117 (in Japanese).
- K. Hepp, Helv. Phys. Acta 45 (1972), 237.
- R. Fukuda, Prog. Theor. Phys. 81 (1989), 34[PTP].
-
L. G. Yaffe, Rev. Mod. Phys. 54 (1982), 407[APS].
-
J. R. Klauder, J. Math. Phys. 4 (1963), 1055[CrossRef];
ibid. 4 (1963), 1058[CrossRef];
ibid. 5 (1964), 177[CrossRef].
A. O. Barut and L. Girardello, Commun. Math. Phys. 21 (1971), 41[CrossRef].
A. M. Perelomov, Commun. Math. Phys. 26 (1972), 222[CrossRef];
ibid. 44 (1975), 197[CrossRef].
R. Gilmore, Ann. of Phys. 74 (1972), 391[CrossRef].
E. H Lieb, Commun. Math. Phys. 31 (1973), 327[CrossRef].
F. A. Berezin, Commun. Math. Phys. 63 (1978), 131[CrossRef].
B. Simon, Commun. Math. Phys. 71 (1980), 247[CrossRef].
- S. Machida and M. Namiki, Proc. Int. Symp. on Foundations of Quantum Mechanics, ed.
S. Kamefuchi, H. Ezawa, Y. Murayama, M. Namiki, S. Nomura, Y. Ohnuki and T. Yajima (Phys. Soc. Jpn, Tokyo, 1984), p. 136.
- N. R. Wallach, Harmonic Analysis on Homogeneous Spaces (Marcel Dekker, Inc., New York, 1973).
- A. A. Kirillov, Elements of the Theory of Representaions (Springer Verlag, Berlin, 1976).
- S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82 (1989), 246[PTP].
Citing Article(s) :
-
Journal of the Physical Society of Japan 69 (2000) pp. 73-87
:
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Dynamical Processes in Exactly Solvable Quantum Mechanical Systems I.
-
Sachiko Kitajima and Fumiaki Shibata
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Progress of Theoretical Physics Vol. 84 No. 2 (1990) pp. 195-202
:
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A Model of the Cloud Chamber in Generalized Coherent State Formalism
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Kiyotaka Kakazu
-
Progress of Theoretical Physics Vol. 86 No. 4 (1991) pp. 943-958
:
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One-Particle Detectors with SU(1, 1) Coherent States in Quantum Measurement
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Kiyotaka Kakazu and Akihiko Ogawa
-
Progress of Theoretical Physics Vol. 87 No. 1 (1992) pp. 61-76
:
-
The Wigner-Araki-Yanase Theorem and Its Extension in Quantam Measurement with Generalized Coherent States
-
Shoju Kudaka and Kiyotaka Kakazu
