Temporal behavior of quantum mechanical systems

International Journal of Modern Physics B

Volumn 10, Issue 3, 1996, Pages 247-295

  Nakazato, Hiromichi ^a   Namiki, Mikio ^a   Pascazio, Saverjo ^b,c  

^a WASEDA UNIVERSITY   (Japan)

^b UNIVERSITY OF BARI   (Italy)

^c INFN SEZIONE DI BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000606327     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979296000118     Document Type: Article

References (107)

1. V. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930); 65, 18 (1930).
2. V. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930); 65, 18 (1930).
3. G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936).
4. G. Gamow, Z. Phys. 51, 204 (1928).
5. V. Fock and N. Krylov, Journal of Physics 11, 112 (1947).
6. L. A. Khalfin, Dokl. Acad. Nauk USSR 115, 277 (1957) [Sov. Phys. Dokl. 2, 340 (1957)]; Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)].
7. L. A. Khalfin, Dokl. Acad. Nauk USSR 115, 277 (1957) [Sov. Phys. Dokl. 2, 340 (1957)]; Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)].
8. L. A. Khalfin, Dokl. Acad. Nauk USSR 115, 277 (1957) [Sov. Phys. Dokl. 2, 340 (1957)]; Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)].
9. L. A. Khalfin, Dokl. Acad. Nauk USSR 115, 277 (1957) [Sov. Phys. Dokl. 2, 340 (1957)]; Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)].
10. R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain (American Mathematical Society Colloquium Publications XIX, New York, 1934).
11. E. J. Hellund, Phys. Rev. 89, 919 (1953).
12. M. Namiki and N. Mugibayashi, Prog. Theor. Phys. 10, 474 (1953).
13. H. Araki, Y. Munakata, M. Kawaguchi and T. Goto, Prog. Theor. Phys. 17, 419 (1957).
14. T. D. Lee, Phys. Rev. 95, 1329 (1954).
15. J. Schwinger, Ann. Phys. 9, 169 (1960).
16. L. Fonda, G. C. Ghirardi and A. Rimini, Rep. Prog. Phys. 41, 587 (1978).
17. G-C. Cho, H. Kasari and Y. Yamaguchi, Prog. Theor. Phys. 90, 803 (1993).
18. G-C. Cho, H. Kasari and Y. Yamaguchi, Prog. Theor. Phys. 91, 1259 (1994).
19. C. B. Chiu, E. C. G. Sudarshan and G. Bhamathi, Phys. Rev. D46, 3508 (1992).
20. L. P. Horwitz, Found. Phys. 25, 39 (1995).
21. W. Heitler, The Quantum Theory of Radiation (Clarendon Press, Oxford, 3rd ed., 1954).
22. E. Arnous and S. Zienau, Helv. Phys. Acta 34, 279 (1951).
23. H. Nakazato, M. Namiki, S. Pascazio and H. Rauch, Phys. Lett. A199, 27 (1995).
24. J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932) [English translation: Mathematical Foundations of Quantum Mechanics, translated by E. T. Beyer (Princeton University Press, Princeton, 1955)].
25. J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932) [English translation: Mathematical Foundations of Quantum Mechanics, translated by E. T. Beyer (Princeton University Press, Princeton, 1955)].
26. For a review, see Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek (Princeton University Press, New Jersey, 1983).
27. P. Busch, P. J. Lahti and P. Mittelstaedt, The Quantum Theory of Measurement (Springer-Verlag, Berlin, 1991).
28. A. Beskow and J. Nilsson, Arkiv för Fysik 34, 561 (1967).
29. L. A. Khalfin, Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Letters 8, 65 (1968)]; Phys. Lett. B112, 223 (1982); Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].
30. L. A. Khalfin, Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Letters 8, 65 (1968)]; Phys. Lett. B112, 223 (1982); Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].
31. L. A. Khalfin, Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Letters 8, 65 (1968)]; Phys. Lett. B112, 223 (1982); Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].
32. L. A. Khalfin, Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Letters 8, 65 (1968)]; Phys. Lett. B112, 223 (1982); Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].
33. L. A. Khalfin, Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Letters 8, 65 (1968)]; Phys. Lett. B112, 223 (1982); Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].
34. L. Fonda, G. C. Ghirardi, A. Rimini and T. Weber, Nuovo Cimento A15, 689 (1973); A18, 805 (1973); A. DeGasperis, L. Fonda and G. C. Ghirardi, Nuovo Cimento A21, 471 (1974).
35. L. Fonda, G. C. Ghirardi, A. Rimini and T. Weber, Nuovo Cimento A15, 689 (1973); A18, 805 (1973); A. DeGasperis, L. Fonda and G. C. Ghirardi, Nuovo Cimento A21, 471 (1974).
36. L. Fonda, G. C. Ghirardi, A. Rimini and T. Weber, Nuovo Cimento A15, 689 (1973); A18, 805 (1973); A. DeGasperis, L. Fonda and G. C. Ghirardi, Nuovo Cimento A21, 471 (1974).
37. B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18, 756 (1977).
38. R. J. Cook, Phys. Scr. T21, 49 (1988).
39. W. H. Itano, D. J. Heinzen, J. J. Bollinger and D. J. Wineland, Phys. Rev. A41, 2295 (1990).
40. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
41. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
42. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
43. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
44. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
45. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
46. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
47. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
48. T. Petrosky, S. Tasaki and I. Prigogine, Phys. Lett. A151, 109 (1990); Physica A170, 306 (1991); A. Peres and A. Ron, Phys. Rev. A42, 5720 (1990); L. E. Ballentine, Phys. Rev. A43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A43, 5168 (1991); V. Frerichs and A. Schenzle, Phys. Rev. A44, 1962 (1991); S. Inagaki, M. Namiki and T. Tajiri, Phys. Lett. A166, 5 (1992); D. Home and M. A. B. Whitaker, Phys. Lett. A173, 327 (1993); Ph. Blanchard and A. Jadczyk, Phys. Lett. A183, 272 (1993).
49. S. Pascazio, M. Namiki, G. Badurek and H. Rauch, Phys. Lett A179, 155 (1993); S. Pascazio and M. Namiki, Phys. Rev. A50, 4582 (1994).
50. S. Pascazio, M. Namiki, G. Badurek and H. Rauch, Phys. Lett A179, 155 (1993); S. Pascazio and M. Namiki, Phys. Rev. A50, 4582 (1994).
51. S. Machida and M. Namiki, Prog. Theor. Phys. 63, 1457, 1833 (1980); M. Namiki, Found. Phys. 18, 29 (1988).
52. S. Machida and M. Namiki, Prog. Theor. Phys. 63, 1457, 1833 (1980); M. Namiki, Found. Phys. 18, 29 (1988).
53. M. Namiki and S. Pascazio, Phys. Rev. A44, 39 (1991); Physics Reports 232, 301 (1993); M. Namiki, S. Pascazio and C. Schiller, Phys. Lett. A182, 17 (1994).
54. M. Namiki and S. Pascazio, Phys. Rev. A44, 39 (1991); Physics Reports 232, 301 (1993); M. Namiki, S. Pascazio and C. Schiller, Phys. Lett. A182, 17 (1994).
55. M. Namiki and S. Pascazio, Phys. Rev. A44, 39 (1991); Physics Reports 232, 301 (1993); M. Namiki, S. Pascazio and C. Schiller, Phys. Lett. A182, 17 (1994).
56. L. van Hove, Physica 21, 517 (1955).
57. C. Bloch, Nucl. Phys. 4, 503 (1957); M. Namiki, Prog. Theor. Phys. 23, 629 (1960).
58. C. Bloch, Nucl. Phys. 4, 503 (1957); M. Namiki, Prog. Theor. Phys. 23, 629 (1960).
59. M. Mizutani, S. Muroya and M. Namiki, Phys. Rev. D37, 3033 (1988).
60. H. Nakazato, M. Namiki and S. Pascazio, Phys. Rev. Lett. 73, 1063 (1994).
61. K. Hepp, Helv. Phys. Acta 45, 237 (1972); J.S. Bell, Helv. Phys. Acta 48, 93 (1975); S. Machida and M. Namiki, in Proc. Int. Symp. on Foundations of Quantum Mechanics, eds. S. Kamefuchi et al. (Phys. Soc. Japan, Tokyo, 1984) p. 136; S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82, 665 (1989). M. Namiki and S. Pascazio, Found. Phys. Lett. 4, 203 (1991).
62. K. Hepp, Helv. Phys. Acta 45, 237 (1972); J.S. Bell, Helv. Phys. Acta 48, 93 (1975); S. Machida and M. Namiki, in Proc. Int. Symp. on Foundations of Quantum Mechanics, eds. S. Kamefuchi et al. (Phys. Soc. Japan, Tokyo, 1984) p. 136; S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82, 665 (1989). M. Namiki and S. Pascazio, Found. Phys. Lett. 4, 203 (1991).
63. K. Hepp, Helv. Phys. Acta 45, 237 (1972); J.S. Bell, Helv. Phys. Acta 48, 93 (1975); S. Machida and M. Namiki, in Proc. Int. Symp. on Foundations of Quantum Mechanics, eds. S. Kamefuchi et al. (Phys. Soc. Japan, Tokyo, 1984) p. 136; S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82, 665 (1989). M. Namiki and S. Pascazio, Found. Phys. Lett. 4, 203 (1991).
64. K. Hepp, Helv. Phys. Acta 45, 237 (1972); J.S. Bell, Helv. Phys. Acta 48, 93 (1975); S. Machida and M. Namiki, in Proc. Int. Symp. on Foundations of Quantum Mechanics, eds. S. Kamefuchi et al. (Phys. Soc. Japan, Tokyo, 1984) p. 136; S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82, 665 (1989). M. Namiki and S. Pascazio, Found. Phys. Lett. 4, 203 (1991).
65. K. Hepp, Helv. Phys. Acta 45, 237 (1972); J.S. Bell, Helv. Phys. Acta 48, 93 (1975); S. Machida and M. Namiki, in Proc. Int. Symp. on Foundations of Quantum Mechanics, eds. S. Kamefuchi et al. (Phys. Soc. Japan, Tokyo, 1984) p. 136; S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82, 665 (1989). M. Namiki and S. Pascazio, Found. Phys. Lett. 4, 203 (1991).
66. H. Nakazato and S. Pascazio, Phys. Rev. Lett. 70, 1 (1993); Phys. Rev. A48, 1066 (1993).
67. H. Nakazato and S. Pascazio, Phys. Rev. Lett. 70, 1 (1993); Phys. Rev. A48, 1066 (1993).
68. H. Nakazato and S. Pascazio, "On the short-time behavior of quantum mechanical systems", preprint 1994.
69. B. Russell, A History of Western Philosophy (George Allen & Unwin, London, 1946).
70. J. von Neumann, Ref. 20, p. 195 [p. 366 of the English translation]. See also the paper by A. Peres and A. Ron in Ref. 29.
71. E. P. Wigner, Am. J. Phys. 31, 6 (1963).
72. J. Summhammer, G. Badurek, H. Rauch, U. Klischko and A. Zeilinger, Phys. Rev. A27, 2523 (1983); G. Badurek, H. Rauch and J. Summhammer, Phys. Rev. Lett. 51, 1015 (1983).
73. J. Summhammer, G. Badurek, H. Rauch, U. Klischko and A. Zeilinger, Phys. Rev. A27, 2523 (1983); G. Badurek, H. Rauch and J. Summhammer, Phys. Rev. Lett. 51, 1015 (1983).
74. A. Peres, Am. J. Phys. 48, 931 (1980).
75. P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger and M. Kasevich, in Fundamental Problems in Quantum Theory, eds. D. M. Greenberger and A. Zeilinger (Ann. N. Y. Ac. Sci. 755, New York, 1995) p. 383.
76. G. C. Ghirardi, C. Omero, T. Weber and A. Rimini, Nuovo Cimento A52, 421 (1979).
77. L. S. Schulman, A. Ranfagni and D. Mugnai, Phys. Scr. 49, 536 (1994).
78. L. A. Khalfin, Phys. Lett. B112, 223 (1982); C. B. Chiu, B. Misra and E. C. G. Sudarshan, Phys. Lett. B117, 34 (1982); L. Fonda, G. C. Ghirardi and T. Weber, Phys. Lett. B131, 309 (1983); L. P. Horwitz and E. Katznelson, Phys. Rev. Lett. 50, 1184 (1983); C. Bernardini, L. Maiani and M. Testa, Phys. Rev. Lett. 71, 2687 (1993).
79. L. A. Khalfin, Phys. Lett. B112, 223 (1982); C. B. Chiu, B. Misra and E. C. G. Sudarshan, Phys. Lett. B117, 34 (1982); L. Fonda, G. C. Ghirardi and T. Weber, Phys. Lett. B131, 309 (1983); L. P. Horwitz and E. Katznelson, Phys. Rev. Lett. 50, 1184 (1983); C. Bernardini, L. Maiani and M. Testa, Phys. Rev. Lett. 71, 2687 (1993).
80. L. A. Khalfin, Phys. Lett. B112, 223 (1982); C. B. Chiu, B. Misra and E. C. G. Sudarshan, Phys. Lett. B117, 34 (1982); L. Fonda, G. C. Ghirardi and T. Weber, Phys. Lett. B131, 309 (1983); L. P. Horwitz and E. Katznelson, Phys. Rev. Lett. 50, 1184 (1983); C. Bernardini, L. Maiani and M. Testa, Phys. Rev. Lett. 71, 2687 (1993).
81. L. A. Khalfin, Phys. Lett. B112, 223 (1982); C. B. Chiu, B. Misra and E. C. G. Sudarshan, Phys. Lett. B117, 34 (1982); L. Fonda, G. C. Ghirardi and T. Weber, Phys. Lett. B131, 309 (1983); L. P. Horwitz and E. Katznelson, Phys. Rev. Lett. 50, 1184 (1983); C. Bernardini, L. Maiani and M. Testa, Phys. Rev. Lett. 71, 2687 (1993).
82. L. A. Khalfin, Phys. Lett. B112, 223 (1982); C. B. Chiu, B. Misra and E. C. G. Sudarshan, Phys. Lett. B117, 34 (1982); L. Fonda, G. C. Ghirardi and T. Weber, Phys. Lett. B131, 309 (1983); L. P. Horwitz and E. Katznelson, Phys. Rev. Lett. 50, 1184 (1983); C. Bernardini, L. Maiani and M. Testa, Phys. Rev. Lett. 71, 2687 (1993).
83. A. Messiah, Mécanique Quantique I, II (Dunod, Paris, 1959) [Quantum Mechanics I, II (North-Holland, Amsterdam, 1961)].
84. A. Messiah, Mécanique Quantique I, II (Dunod, Paris, 1959) [Quantum Mechanics I, II (North-Holland, Amsterdam, 1961)].
85. E. Fermi, Nuclear Physics (Univ. Chicago Press, Chicago, 1950) p. 136, 148; See also Fermi's Notes on Quantum Mechanics. A Course Given at the University of Chicago in 1954, edited by E. Segré (Univ. Chicago Press, Chicago, 1960) lecture 23; E. Fermi, Rev. Mod. Phys. 4, 87 (1932).
86. E. Fermi, Nuclear Physics (Univ. Chicago Press, Chicago, 1950) p. 136, 148; See also Fermi's Notes on Quantum Mechanics. A Course Given at the University of Chicago in 1954, edited by E. Segré (Univ. Chicago Press, Chicago, 1960) lecture 23; E. Fermi, Rev. Mod. Phys. 4, 87 (1932).
87. E. Fermi, Nuclear Physics (Univ. Chicago Press, Chicago, 1950) p. 136, 148; See also Fermi's Notes on Quantum Mechanics. A Course Given at the University of Chicago in 1954, edited by E. Segré (Univ. Chicago Press, Chicago, 1960) lecture 23; E. Fermi, Rev. Mod. Phys. 4, 87 (1932).
88. P. Exner, Open Quantum Systems and Feynman Integrals (Reidel, Dordrecht, 1985), Chapter I and especially the notes to Sec. 1.5.
89. W. Pauli, Festschrift zum 60. Geburtstage A. Sommerfelds (Hirzel, Leipzig, 1928) p. 30.
90. M. Namiki, in Quantum Mechanics II, eds. H. Yukawa and T. Toyoda, (Iwanami-Shoten Publ., Tokyo, 1978) p. 162 (in Japanese).
91. E. B. Davies, Commun. Math. Phys. 39, 91 (1974).
92. G. L. Sewell, Quantum Theory of Collective Phenomena (Clarendon Press, Oxford, 1986) p. 74.
93. L. Accardi, A. Frigerio and Y. G. Lu, Commun. Math. Phys. 131, 537 (1990); L. Accardi, Y.G. Lu and I. Volovich, "Non-commutative (quantum) probability, master fields and stochastic bosonization", preprint Volterra ID-9412241 (1994).
94. L. Accardi, A. Frigerio and Y. G. Lu, Commun. Math. Phys. 131, 537 (1990); L. Accardi, Y.G. Lu and I. Volovich, "Non-commutative (quantum) probability, master fields and stochastic bosonization", preprint Volterra ID-9412241 (1994).
95. S. Hayakawa, T. Sasakawa, K. Tomita, M. Yasuno and M. Yokota, Prog. Theor. Phys. 21, 85 (1959).
96. G. Höhler, Z. Phys. 152, 546 (1958). Also see, B. Zumino, in Lectures in Field Theory and the Many-Body Problem, ed. E. R. Caianiello (Academic Press, New York, 1961) p. 37; M. Lévy, ibid., p. 47.
97. G. Höhler, Z. Phys. 152, 546 (1958). Also see, B. Zumino, in Lectures in Field Theory and the Many-Body Problem, ed. E. R. Caianiello (Academic Press, New York, 1961) p. 37; M. Lévy, ibid., p. 47.
98. G. Höhler, Z. Phys. 152, 546 (1958). Also see, B. Zumino, in Lectures in Field Theory and the Many-Body Problem, ed. E. R. Caianiello (Academic Press, New York, 1961) p. 37; M. Lévy, ibid., p. 47.
99. P. L. Knight and P. W. Milonni, Phys. Lett. A56, 275 (1976).
100. M. Havliček, quoted in Ref. 51, p. 103.
101. K. Hiyama and S. Takagi, Phys. Rev. A48, 2568 (1993).
102. N. N. Bogoliubov and D. V. Shirkov, Quantum Fields (Benjamin Cummings, Massachusetts, 1983) p. 331.
103. C. P. Sun, Phys. Rev. A48, 898 (1993).
104. W. Pauli, Handbuch der Physik, ed. S. Flügge (Springer-Verlag, Berlin, 1958), 5/1, 60; T. Goto, K. Yamaguchi and N. Sudo, Prog. Theor. Phys. 66, 1525 (1981).
105. W. Pauli, Handbuch der Physik, ed. S. Flügge (Springer-Verlag, Berlin, 1958), 5/1, 60; T. Goto, K. Yamaguchi and N. Sudo, Prog. Theor. Phys. 66, 1525 (1981).
106. A. J. Leggett, in Proc. 4th Int. Symp. on Foundations of Quantum Mechanics, eds. M. Tsukada et al. (Phys. Soc. Japan, Tokyo, 1993) p. 10.
107. M. Berry, in Fundamental Problems in Quantum Theory, eds. D.M. Greenberger and A. Zeilinger (Ann. N. Y. Ac. Sci. Vol. 755, New York, 1995) p. 303. See also the interesting discussion on the QZE in this paper.