A new look at the derivation of the Schrödinger equation from Newtonian mechanics

Annalen der Physik (Leipzig)

Volumn 12, Issue 6, 2003, Pages 371-402

  Fritsche, L ^a   Haugk, M ^b  

^a CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

^b Hewlett Packard GmbH   (Germany)

Author keywords

Schr dinger equation; Stochastic quantum mechanics; Vacuum fluctuations

Indexed keywords

ATOMS; BROWNIAN MOVEMENT; DIFFRACTION; ELECTRON TUNNELING; EQUATIONS OF MOTION; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY;

NEWTONIAN MECHANICS; SCHRODINGER EQUATION; STOCHASTIC FORCES;

QUANTUM THEORY;

EID: 0042660883     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/andp.200310017     Document Type: Article

References (56)

1. J. Bell, Phys. World 3 8 (August), 33 (1990).
2. E. Nelson, J. Math. Phys. 5, 332 (1964)
3. E. Nelson, Phys. Rev. 150, 1079 (1966).
4. J. G. Gilson, Proc. Camb. Phil. Soc. 64, 1061 (1968).
5. L. S. F. Olavo, Phys. Rev. A 61, 052109 (2000).
6. P. Blanchard et al. (eds.), Mathematical and Physical Aspects of Stochastic Mechanics (Springer, Heidelberg, 1987).
7. K. Yasue, Int. J. Theor. Phys. 18, 861 (1979).
8. L. De La Peña, Found. Phys. 12, 1017 (1982).
9. A. Zeilinger, Phys. Today 52 (February), 13 (1999).
10. W. Heisenberg, Physics and Philosophy (Harper and Row, New York, 1958), p. 129.
11. W. Heisenberg, The Physicist's Conception of Nature, translated by A. J. Pomerans (Hartcourt Brace, New York, 1958), p. 15
12. S. Goldstein, Phys. Today 51 (March), 42 (1998).
13. I. Fényes, Z. Physik 132, 81 (1951).
14. W. Weizel, Z. Physik 134, 264 (1953)
15. W. Weizel, Z. Physik 135, 270 (1953)
16. W. Weizel, Z. Physik 136, 582 (1954).
17. D. Kershaw, Phys. Rev. B 136, 1850 (1964).
18. G. G. Comisar, Phys. Rev. B 138, 1332 (1965).
19. E. Nelson, Dynamical Theories of Brownian Motion (Princeton University Press, New Jersey, 1967).
20. E. Nelson, Quantum Fluctuations (Princeton University Press, New Jersey, 1985).
21. F. Selleri and G. Tarozzi, Riv. Nuovo Cimento 4 (2), (1981).
22. D. Bohm and B. J. Hiley, Phys. Rep. 172, 93 (1989).
23. L. de Broglie, C.R. Acad. Sci. (Paris) 183, 447 (1926)
24. L. de Broglie, C.R. Acad. Sci. (Paris) 184, 273 (1927)
25. L. de Broglie, C.R. Acad. Sci. (Paris) 185, 380 (1927)
26. L. de Broglie, The Current Interpretation of Quantum Mechanics: a Critical Study (Cambridge University Press, Cambridge, 1965).
27. D. Bohm, Quantum Theory (Prentice Hall, Englewood Cliffs, New Jersey, 1951).
28. D. Bohm, Phys. Rev. 85, 166 (1952)
29. D. Bohm, Phys. Rev. 85, 180 (1952).
30. D. Bohm, Phys. Rev. 89, 458 (1953).
31. D. Bohm, in: Quantum Theory, Vol. 3, edited by D. R. Bates (Academic Press, New York, 1962).
32. D. Bohm and J. P. Vigier, Phys. Rev. 96, 208 (1954).
33. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, Phys. Rev. Lett. 88, 100404 (2002).
34. M. Requardt, The Underlying Substructure of Quantum Theory and the Real Nature of Quantum Phase Interference. A Natural Resolution of the Einstein-Podolski-Rosen Paradox, the Double-Slit Experiment etc. A New Stochastic-Geometric Conception of Microdynamics and Force. Unpublished manuscript, Göttingen (1981).
35. M. J. W. Hall and M. Reginatto, J. Phys. A, Math. Gen. 35, 3289 (2002).
36. A. Einstein, Ann. Phys. (Germany) 17, 549 (1905)
37. A. Einstein, Ann. Phys. (Germany) 19, 371 (1906)
38. A. Einstein, Investigation on the Theory of the Brownian Movement, translated by A. D. Cowper (Methuen and Company, London, 1926).
39. P. Langevin, C.R. Acad. Sci. (Paris) 146, 530 (1908).
40. M. V. Smoluchowski, Ann. Phys. 21, 756 (1906)
41. M. V. Smoluchowski, Ann. Phys. 48, 1103 (1915)
42. Abhandlungen über die Brownische Bewegung und verwandte Erscheinungen (Akademische Verlagsgesellschaft, Leipzig, 1923).
43. A. D. Fokker, Ann. Phys. 43, 812 (1914).
44. M. Planck, Sitz. der Preuß. Akademie 324 (1917).
45. A. N. Kolmogorov, Math. Ann. 104, 415 (1931).
46. H. Gebelein, Turbulenz (Springer, Berlin,1935), p. 75.
47. H. Helmholtz, Crelles J. 55, 25 (1858).
48. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
49. G. Möllenstedt and W. Bayh, Phys. Bl. 18, 299 (1962).
50. R. G. Chambers, Phys. Rev. Lett. 5, 3 (1960).
51. B. Mielnik and G. Tengstrand, Int. J. Theor. Phys. 19, 239 (1980).
52. J. v. Neumann, Mathematical Foundation of Quantum Mechanics, translated by R. T. Beyer (Princeton University Press, Princeton, New Jersey, 1955).
53. J. S. Bell, Rev. Mod. Phys. 38, 447 (1966).
54. J. S. Bell, Physics 1, 195 (1964).
55. G. Hermann, Abhandlungen der Freis'schen Schule 6, 75 (1935).
56. N. D. Mermin, Rev. Mod. Phys. 65, 803 (1993).