臺灣博碩士論文加值系統

根據一個量子力學的詮釋 ‘隨機解釋’，我們提出兩個理論以呈現幾個量子力學的蘊涵‧其一是隨機介質模型理論‧在這個模型，微觀粒子的量子漲落被假設是源自微觀粒子與隨機介質間的碰撞‧我們限定此碰撞遵守幾個特性以確保此模型能重新產生薛丁格波動力學的統計系綜表述‧藉由此模型，我們得到幾類微觀粒子能和微觀粒子與隨機介質間的局部傳輸能之型式‧
另一個理論是隨機微觀相空間構式‧我們提出一組描述個別微觀粒子運動狀態的隨機動力學方程式‧根據這組方程式，我們得到一個馮紐曼崩塌過程的動力學表述‧再者，此微觀相空間構式存在負機率‧根據隨機動力性質，我們將研究其機制‧一些關於能量量子化與非局域性本質之認知也一併在此討論‧

Based on the framework of stochastic interpretation for quantum mechanics, two approaches are proposed to present several implications of quantum mechanics. One is the microscopic transport conservation approach for the random medium model. In this model, the quantum fluctuation of the microscopic object is assumed to arise from the collision between the microscopic object and the medion. Some assumptions for the object-medion collision are proposed to guarantee that the statistical ensemble manifestation of Schrodinger wave mechanics can be reproduced. According to this approach, several kinds of microscopic object energies and the local energy transport between the objects and the medions are studied.
The other approach is the stochastic microscopic-phase-space formulation. A set of stochastic dynamic equations describing the motion of the individual object are proposed. According to this set of equations, a dynamic description for the von Neumann collapse is presented. Moreover, there exists the negativity of the microscopic-phase-space description in this formulation. The mechanism of the negativity is studied according to the stochastic dynamics. Some discussions on the significance of energy quantization and non-locality are also presented here.

Introduction
Preview
Stochastic mechanics
Nelson theory
Interference and stochastic-mechanics transition probability
Relaxation processes, quantization and quantum measurement
Weyl-Wigner-Moyal phase-space formulation
WWM phase-space
Abnormal stochasticity without Brownian diffusion
Random medium model
Microscopic transport conservation approach
Momentum statistical moment and object energies
Discussion
Transport energy and local transport phenomenon
Binding energy and non-local potential
Energy quantization
Stochastic micro-phase-space formulation
Stochastic dynamics
Forward dynamic equations
Backward dynamic equations
Situations specified by quantum mechanics
Bracket forms and local transport phenomenon
Dynamic description for von Neumann collapse
Connection with wave mechanics
Energy conservation of object ensemble
Implication of Negativity
Summary and prospect
Appendix
Nelson processes
Example for micro-stochastic equation

1. E. Nelson, Phys. Rev.150, 1079 (1966).
2. F. Guerra, Phys. Rep.77, 263 (1981).
3. D. de Falco, S. De Martino and S. De Siena,Phys. Rev. Lett.49, 181 (1982).
4. K. Yasue, J. Math. Phys.22, 1010 (1981); J. C. Zambrini, Int. J. Theor. Phys.24, 277 (1985).
5. G. Badurek, H. Rauch and J. Summhammer, Phys. Rev. Lett.51, 1015 (1983); C. Dewdney, Ph. Gueret, A. Kyprianidis and J. P. Vigier, Phys. Lett. A102, 291 (1984); C. Dewdney, A. Garuccio, A. Kyprianidis and J. P. Vigier, Phys. Lett. A104, 325 (1984).
6. M. S. Wang, Phys. Rev. A 38, 5401 (1988).
7. D. Bohm and B. J. Hiley, Phys. Rep.172, 93 (1989).
8. B. J. Hiley and F. D. Peat, Quantum Implications, Routledge & Kegan Paul, New York, (1991).
9. P. Garbaczewski, Phys. Lett. A162, 129 (1992); P. Garbaczewski and J. P. Vigier, Phys. Rev. A46, 4634 (1992).
10. C. L. Wu, Chin. J. Phys. 35, 866 (1997).
11. L. S. F. Olavo, Physica A262, 197 (1999); Phys. Rev. A61, 052109 (2000).
12. D. Bohm and J. P. Vigier, Phys. Rev. 96, 208 (1954).
13. B. S. DeWitt, in General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel, Cambridge University Press (1967).
14. J.-P. Vigier, Astron. Nachr.303, 55 (1982).
15. D. Bohm, Phys. Rev. 85, 166, 180 (1952).
16. E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press (1967).
17. E. Nelson, Quantum Fluctuations, Princeton University Press (1985).
18. D. Bohm, The Undivided Universe, New York (1993).
19. J.-P. Vigier, C. Dewdney, P. R. Holland and A. Kyprianidis, in Ref.[8].
20. M. T. Lee, Physica A,308, 29 (2002).
22. The discussion with C. L. Wu.
23. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955).
24. V. B. Braginsky and F. Y. Khalili, quantum Measurement, ed. K. S. Thorne, Cambridge University Press (1992).
25. E. R. Loubenets, J. Phys. A, 34, 7639 (2001), 35, 565 (2002); G. M. D''Ariano and M. F. Sacchi, Phys. Lett. A 231, 325 (1997); D. Sokolovski, Phys. Rev. Lett. 79, 4946 (1997); Y. Liu and D. Sokolovski, Phys. Rev. A63, 014102 (2000); Y. Aharonov and L. Vaidman, Phys. Rev. A41, 11 (1990); D. A. R. Dalvit, J. Dziarmaga and W. H. Zurek, Phys. Rev. Lett. 86, 373 (2001); G. M. D''Ariano and L. Maccone, Phys. Rev. Lett. 80, 5465 (1998).
26. P. Blanchard, S. Golin and M. Serva, Phys. Rev. D 34, 3732 (1986); C. M. Caves and G. J. Milburn, Phys. Rev. A 36, 5543 (1987); M. S. Wang, Phys. Rev. Lett. 79, 3319 (1997); M. Pavon, J. Math. Phys. 40, 5565 (1999); T. Bhattacharya, S. Habib and K. Jacobs, Eprint: quant-ph/9906092.
27. E. P. Wigner, Phys. Rev. 40, 749 (1932).
28. L. de Broglie, compt. Rend. 183, 447 (1926); 184, 273 (1927); 185, 380 (1927).
29. A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935).
30. Y. Mizobuchi and Y. Ohtake, Phys. Lett. A 168, 1 (1992).
31. R. Furth, Z. Physik 81, 143 (1933).
32. I. Fenyes, Z. Physik 132, 81 (1952); W. Weizel, Z. Physik 134, 264 (1953); 135, 270 (1953); 136, 582 (1954).
33. G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).
34. P. Garbaczewski, Phys. Lett. A 164, 6 (1992).
35. H. Risken, The Fokker-Planck Equation, Springer-Verlag, New York (1989), chapter 2-4.
36. P. E. Kloeden and E. Platen, Numerical Solution of stochastic Differential Equation, Springer-Verlag, New York (1992).
37. T. G. Dankel, J. Math. Phys. 18, 253 (1977).
38. D. Dohrn, F. Guerra and P. Ruggiero, Spinning Particles and Relativistic Particles in the Framework of Nelson''s Stochastic Mechanics, in Feynman Path Integrals, ed. S. Albeverio, Lecture Note in Physics 106, Springer (1979); J.-P. Vigier, Found. Phys. 25, 55 (1995).
39. F. Guerra and P. Ruggiero, Phys. Rev. Lett. 31, 1022 (1973); I. Ohba, Prog. Theor. Phys. 77, 1267 (1987); M. Namiki, Stochastic Quantization, Springer (1992); T. M. Samols, Eprint: hep-th/9501117.
40. M. S. Wang, Phys. Rev. A 37, 1036 (1988).
41. L. I. Schiff, Quantum Mechanics, McGraw-Hill, New York (1971).
42. H. Bergeron, J. Math. Phys. 42, 3983 (2001).
43. S. Habib, K. Shizume and W. H. Zuerk, Phys. Rev. Lett. 80, 4361 (1998); W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989); W. H. Zurek, Physica Scripta. T76, 186 (1998); C. Anastopoulos, J. Math. Phys. 42, 3225 (2001).
44. W. M. Zhang, D. H. Feng and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990); W. M. Zhang and D. H. Feng, Phys. Rep. 252, 1 (1995); M. T. Lee, W. M. Zhang and C. L. Wu, Phys. Rev. C 57, 637 (1998).
45. R. F. Fox and C. Elston, Phys. Rev. E 49, 3683 (1994), ibid. 50, 2553 (1994).
46. P. Carruthers and F. Zachariasen, Rev. Mod. Phys. 55, 245 (1983).
47. C. W. Gardiner, Quantum Noise, Springer-Verlag, New York (1991); D. T. Smithey, M. Beck and M. G. Raymer, Phys. Rev. Lett. 70, 1244 (1993).
48. H. Weyl, Gruppentheorie und Quantenmechanik (1931), p. 244.
49. J. E. Mayal, Proc. Cambridge Phil. Soc. 45, 99 (1949); T. Takabayasi, Prog. Theor. Phys. 11, 341 (1954).
50. N. L. Balazs and B. K. Jennings, Phys. Rep. 104, 347 (1984).
51. M. Hillery, R. F. O''connell, M. O. Scully and E. P. Winger, Phys. Rep. 106, 121 (1984); Y. S. Kim and M. E. Noz, phase-space Picture of Quantum Mechanics, World Scientific, Singapore (1991).
52. L. Cohen, J. Math. Phys. 7, 781 (1966); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); H. W. Lee, Phys. Rep. 259, 147 (1995).
53. D. Bohm and B. J. Hiley, Found. Phys. 11, 179 (1981).
54. N. C. Dias and J. N. Prata, Phys. Lett. A, 291, 355 (2001).
55. J.-P. Amiet and S. Weigert, Phys. Rev. A, 63, 012102 (2001); P. Kasperkovitz and M. Peev, Ann. Phys. 230, 21 (1994).
56. E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime, D. Reidel, Boston (1985); J.-P. Amiet and M. B. Cibils, J. Phys. A. 24, 1515 (1991); F. Antonsen, Eprint: quant-ph/9608042.
57. C. Brif and A. Mann, Phys. Rev. A, 59, 971 (1999).
58. K. Huang, Statistical Mechanics, Wiley, New York (1987), chapter 3-5.
59. H. Goldstein, Classical Mechanics, Addison-Wesley (1980).
60. K. Yasue, J. Math. Phys. 23, 1583 (1981).
61. K. Ito, Extension of Stochastic Integrals, in Proc. Intern. Symp. SDE, Kyoto 1976, edited by K. Ito (Wiley, New York, 1978).