Skip to main content
SpringerLink
Log in

Generic Bohmian Trajectories of an Isolated Particle

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de Polavieja. The reasons why the latter tend to be much more nearly classical are discussed. The implications for other trajectory interpretations are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. D. Bohm, Phys. Rev. 85, 166, 180 (1952).

    Google Scholar 

  2. D. Bohm and B. J. Hiley, The Undivided Universe (Routledge, London, 1993).

    Google Scholar 

  3. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

    Google Scholar 

  4. P. R. Holland, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A. Fine, and S. Goldstein, eds. (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  5. P. R. Holland, Found. Phys. 28, 881 (1998).

    Google Scholar 

  6. B.-G. Englert, M. O. Scully, G. Süssmann, and H. Walther, Z. Naturforsch 47a, 1175 (1992).

    Google Scholar 

  7. D. Dürr, W. Fusseder, S. Goldstein, and N. Zanghi, Z. Naturforsch 48a, 1261 (1993).

    Google Scholar 

  8. B.-G. Englert, M. O. Scully, G. Süssmann, and H. Walther, Z. Naturforsch 48a, 1263 (1993).

    Google Scholar 

  9. C. Dewdney, L. Hardy, and E. J. Squires, Phys. Lett. A 184, 6 (1993).

    Google Scholar 

  10. Y. Aharanov and L. Vaidman, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A. Fine, and S. Goldstein, eds. (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  11. M. O. Scully, Physica Scripta T 76, 41 (1998).

    Google Scholar 

  12. R. B. Griffiths, Los Alamos e-print, xxx.lanl.gov, quant-ph/9902059.

  13. A. Fine, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A. Fine, and S. Goldstein, eds. (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  14. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).

    Google Scholar 

  15. D. N. Page, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A. Fine, and S. Goldstein, eds. (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  16. E. J. Squires, personal communication.

  17. F. Schrödinger, Naturwissenschaften 23, 807, 823, 844 (1935); reprinted in J. A. Wheeler and W. H. Zurek (eds.), Quantum Theory and Measurement (Princeton University Press, Princeton, N.J., 1983).

    Google Scholar 

  18. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).

    Google Scholar 

  19. R. Omńes, The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994).

    Google Scholar 

  20. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).

    Google Scholar 

  21. W. H. Zurek, Phil. Trans. Roy. Soc. Lond. A 356, 1793 (1998).

    Google Scholar 

  22. H. D. Zeh, Los Alamos e-print, xxx.lanl.gov, quant-ph/9812059.

  23. S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 985 (1953).

    Google Scholar 

  24. D. Bohm and J.-P. Vigier, Phys. Rev. 96, 208 (1954).

    Google Scholar 

  25. D. Bohm and B. J. Hiley, Phys. Rep. 172, 93 (1989).

    Google Scholar 

  26. E. Nelson, Phys. Rev. 150, 1079 (1966).

    Google Scholar 

  27. E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1985).

    Google Scholar 

  28. S. Goldstein, J. Stat. Phys. 47, 645 (1987).

    Google Scholar 

  29. J. C. Vink, Phys. Rev. A 48, 1808 (1993).

    Google Scholar 

  30. S. M. Roy and V. Singh, Mod. Phys. Lett. A 10, 709 (1995).

    Google Scholar 

  31. V. Singh, Pramana 49, 5 (1997).

    Google Scholar 

  32. S. M. Roy and V. Singh, Los Alamos e-print, quant-ph/9811041.

  33. G. Garcia de Polavieja, Phys. Lett. A 220, 303 (1996).

    Google Scholar 

  34. E. R. Floyd, Found. Phys. Lett. 9, 489 (1996).

    Google Scholar 

  35. E. R. Floyd, Int. J. Mod. Phys. A 14, 1111 (1999).

    Google Scholar 

  36. A. E. Faraggi and M. Matone, Los Alamos e-print, hep-th/9809127.

  37. J. Bub, Interpreting the Quantum World (Cambridge University Press, Cambridge, 1997).

    Google Scholar 

  38. R. I. Sutherland, Found. Phys. 27, 845 (1997).

    Google Scholar 

  39. E. Deotto and G. C. Ghirardi, Found. Phys. 28, 1 (1998).

    Google Scholar 

  40. G. Bacciagaluppi, Los Alamos e-print, xxx.lanl.gov, quant-ph/9811040.

  41. G. Potvin, Los Alamos e-print, xxx.lanl.gov, quant-ph/9908019.

  42. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940).

    Google Scholar 

  43. M. Hillery, R. F O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).

    Google Scholar 

  44. H. W. Lee, Phys. Rep. 259, 147 (1995).

    Google Scholar 

  45. E. Arthurs and S. C. Kelly, Bell Syst. Tech. J. 44, 725 (1965).

    Google Scholar 

  46. S. T. Ali and E. Prugovečki, J. Math. Phys. 18, 219 (1977).

    Google Scholar 

  47. P. Busch, M. Grabowski, and P. J. Lahti, Operational Quantum Physics (Springer, Berlin, 1995).

    Google Scholar 

  48. U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, 1997).

    Google Scholar 

  49. D. M. Appleby, Int. J. Theor. Phys. 37, 2557 (1998).

    Google Scholar 

  50. D. M. Appleby, Int. J. Theor. Phys. 38, 807 (1999).

    Google Scholar 

  51. K. B. Møller, T. G. Jørgensen, and G. Torres-Vega, J. Chem. Phys. 106, 7228 (1997).

    Google Scholar 

  52. D. M. Appleby, J. Mod. Opt. 46, 825 (1999).

    Google Scholar 

  53. A. Martin and S. M. Roy, Phys. Lett. B 350, 66 (1995).

    Google Scholar 

Download references

Authors
  1. D. M. Appleby
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Appleby, D.M. Generic Bohmian Trajectories of an Isolated Particle. Foundations of Physics 29, 1863–1883 (1999). https://doi.org/10.1023/A:1018842401049

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018842401049

Keywords

Search

Navigation