Probabilities for histories in nonrelativistic quantum mechanics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 54, Issue 1, 1996, Pages 182-203

  Yamada, Norifumi ^a  

^a CLARKSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000772075     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.54.182     Document Type: Article

References (43)

1. I. Bloch and D. A. Burba, Phys. Rev. D 10, 3206 (1974).
2. D. Marolf, Phys. Rev. A 50, 939 (1994).
3. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
4. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).
5. R. Omnès, J. Stat. Phys. 53, 893 (1988).
6. R. Omnès, J. Stat. Phys. 53, 933 (1988).
7. R. Omnès, J. Stat. Phys. 53, 957 (1988). See also R. Omnès, The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1994).
8. Omitted end note.
9. (a) J. B. Hartle, Phys. Rev. D 44, 3173 (1991); (b) in Gravitation and Quantizations, Proceedings of the Les Houches Summer School, Session LVII, July 1992, edited by B. Julia and J. Zinn-Justin (North-Holland, Amsterdam, 1995).
10. (a) John T. Whelan, Phys. Rev. D 50, 6344 (1994).
11. (b)T. Whelan, Phys. Rev. D 53, 3118 (1996).
12. M. Gell-Mann and J. B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, Singapore, August 1990, edited by K. K. Phua and Y. Yamaguchi (World Scientific, Singapore, 1991).
13. N. Yamada and S. Takagi, Prog. Theor. Phys. 85, 985 (1991).
14. N. Yamada and S. Takagi, Prog. Theor. Phys. 86, 599 (1991).
15. N. Yamada and S. Takagi, Prog. Theor. Phys. 87, 77 (1992).
16. For reviews, see (a) R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994).
17. (b) V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
18. (c) E. H. Hauge and J. A. Støvneng, Rev. Mod. Phys. 61, 917 (1989).
19. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
20. N. Yamada and S. Takagi (Ref. 10), Appendix A; R. D. Sorkin, in Conceptual Problems of Quantum Gravity, edited by A. Ashtekar and J. Stachel (Birkhauser, Boston, 1991), Sec. 3; J. B. Hartle (Ref. 7(a)), Sec. IXtB.
21. J. B. Hartle, Phys. Rev. D 37, 2818 (1988).
22. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).
23. M. Goodman, Am. J. Phys. 49, 843 (1981).
24. For a Euclidean lattice method, see Ref. 16 and also Chap. III of Ref. 20; for a real time lattice method, see N. Yamada and S. Takagi, in Quantum Control and Measurement, Proceedings of the ISQM Satellite Workshop, Japan, 1992, edited by H. Ezawa and Y. Murayama (North-Holland, Amsterdam, 1993).
25. N. Yamada, in Sci. Rep. Tohoku Univ., Ser. 8 12, 177 (1992).
26. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, Exercise 2 in Chap. 4 (translation from the French by G. M. Temmer).
27. L. S. Schulman and R. W. Ziolkowski, in Proceedings of the Third International Conference on Path Integrals from meV to MeV, Bangkok, January 1989, edited by V. Sa-yakanit, W. Sritrakool, J. Berananda, M. C. Gutzwiller, A. Inomata, S. Lundqvist, J. R. Klauder, and L. S. Schulman (World Scientific, Singapore, 1989).
28. A. J. F. Siegert, Phys. Rev. 81, 617 (1951).
29. A. Auerbach and S. Kivelson, Nucl. Phys. B 257, 799 (1985).
30. P. van Baal, in Lectures on Path Integration: Trieste 1991, edited by H. A. Cerdeira, S. Lundqvist, D. Mugnai, A. Ranfagni, V. Sa-yakanit, and L. S. Schulman (World Scientific, Singapore, 1993).
31. M. A. M. de Aguiar, Phys. Rev. A 48, 2567 (1993).
32. D. Sokolovski, Phys. Rev. A 52, R5 (1995).
33. D. Sokolovski and J. N. L. Connor, Phys. Rev. A 47, 4677 (1993).
34. See also D. Sokolovski and J. N. L. Connor, Solid State Commun. 89, 475 (1994).
35. D. Sokolovski, S. Brouard, and J. N. L. Connor, Phys. Rev. A 50, 1240 (1994).
36. Randall S. Dumont and T. L. Marchioro II, Phys. Rev. A 47, 85 (1993).
37. V. S. Olkhovsky and E. Recami (Ref. 13(b)).
38. (a) C. R. Leavens and G. C. Aers, in Scanning Tunneling Microscopy III, edited by R. Wiesendanger and H.-J. Güntherodt (Springer-Verlag, Berlin, 1993).
39. (b) C. R. Leavens, Phys. Lett. A 178, 27 (1993).
40. (c) W. R. McKinnon and C. R. Leavens, Phys. Rev. A 51, 2748 (1995).
41. (d) C. R. Leavens, Found. Phys. 25, 229 (1995).
42. D. Bohm, Phys. Rev. 85, 166, 180 (1952); D. Bohm and B. J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Thgeory(Routledge, London, 1993).
43. C. R Leavens, in Bohmian Mechanics and Quantum Theory: An Appraisal, edited by J. Cushing, A. Fine, and S. Goldstein (Kluwer, Dordrecht, 1996).