New Trajectory Interpretation of Quantum Mechanics

Foundations of Physics

Volumn 28, Issue 6, 1998, Pages 881-911

  Holland, P R ^a  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

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[No Author keywords available]

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EID: 0032395717     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018813112648     Document Type: Article

References (21)

1. L. de Broglie, J. Phys. 8, 225 (1927).
2. D. Bohm, Phys. Rev. 85, 166, 180 (1952).
3. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993), Sec. 3.2.
4. If we extend the question beyond deterministic theories, the answer is surely yes - it is well known that there exist stochastic models describing motion that deviates from (1.1) but which reproduces quantum statistics (and (1.1)) on the average. See, e.g., E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, 1985).
5. D. Dürr, S. Goldstein, and N. Zanghi, J. Stat. Phys. 67, 843 (1992). E. Squires, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Gushing et al. eds. (Kluwer, Dordrecht, 1996) 131. R. J. Sutherland, Found Phys. 27, 845 (1997).
6. D. Dürr, S. Goldstein, and N. Zanghi, J. Stat. Phys. 67, 843 (1992). E. Squires, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Gushing et al. eds. (Kluwer, Dordrecht, 1996) 131. R. J. Sutherland, Found Phys. 27, 845 (1997).
7. D. Dürr, S. Goldstein, and N. Zanghi, J. Stat. Phys. 67, 843 (1992). E. Squires, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Gushing et al. eds. (Kluwer, Dordrecht, 1996) 131. R. J. Sutherland, Found Phys. 27, 845 (1997).
8. E. Deotto and G. C. Ghirardi, Bohmian mechanics revisited, quant-ph/9704021.
9. See e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. García de Polavieja, Phys. Lett. A 200, 303 (1996).
10. See e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. García de Polavieja, Phys. Lett. A 200, 303 (1996).
11. See e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. García de Polavieja, Phys. Lett. A 200, 303 (1996).
12. See e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. García de Polavieja, Phys. Lett. A 200, 303 (1996).
13. See e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. García de Polavieja, Phys. Lett. A 200, 303 (1996).
14. We emphasize that we are simply rewriting the usual complex Hilbert space formalism in terms of real functions. This is not the same as so-called "real" quantum mechanics which uses only the first term on the right-hand side of the scalar product (2.6) and has different physical content. See S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, 1995), p. 44.
15. V. Heine, Group Theory in Quantum Mechanics (Pergamon Press, London, 1960), Chap. 7.
16. In what follows the definition of the Euler angles and the relevant results from the quantum theory of rotators are drawn from Ref. 3, Chap. 10, and references therein.
17. Ref. 3, Sec. 3.9.
18. Ref. 3, Chap. 8.
19. P. R. Holland, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing et al., eds. (Kluwer, Dordrecht, 1996), p. 99.
20. For details, see J. T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (University of Chicago Press, Chicago, 1994), Chap. 8.
21. A. Einstein, Dialectica 2, 120 (1948).