Skip to main content
SpringerLink
Log in

Classical Limit of Quantum Mechanics

  • Chapter
Conceptual Foundations of Quantum Physics

  • 468 Accesses

Abstract

The classical limit problem of quantum mechanics is a particular example of a broader issue concerning the relationship between two physical theories, one empirically valid in a subdomain of the other. It is a basic requirement that a theory superseding the previous one must be compatible with the former at a suitable limit. As a prelude to discussing the classical limit of quantum mechanics, we recall some relevant aspects of this general issue.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Born and O. Wolf, Principles of Optics (Pergamon Press, Oxford, UK, 1980), chap. 3.

    Google Scholar 

  2. H. Bacry and J. M. Levy-Leblond, J. Math. Phys. 9, 1605 (1968).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972), pp. 77–78.

    Google Scholar 

  4. C. Möller, Theory of Relativity (Oxford Univer. Press, Oxford, UK, 1988), pp. 431–33.

    Google Scholar 

  5. P. Holland, Quantum Theory of Motion (Cambridge Univer. Press, Cambridge, 1993), p. 222.

    Book  Google Scholar 

  6. M. V. Berry and K. E. Mount, Rep. Prog. Phys. 35, 315 (1972).

    Article  ADS  Google Scholar 

  7. M. V. Berry, Physica Scripta 40, 335 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. R. L. Liboff, Phys. Today 37, 50 (1984).

    Article  Google Scholar 

  9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1643.

    MATH  Google Scholar 

  10. G. G. Cabrera and M. Kiwi, Phys. Rev. A 36, 2995 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  11. D. Home and S. Sengupta, Nuov. Cim. 82B, 214 (1984).

    MathSciNet  ADS  Google Scholar 

  12. M. Andrews, Am. J. Phys. 44, 1064 (1976).

    Article  ADS  Google Scholar 

  13. M. W. Cole and M. H. Cohen, Phys. Rev. Lett. 23, 1238 (1969).

    Article  ADS  Google Scholar 

  14. A. Messiah, Quantum Mechanics, vol. 1 (North-Holland, Amsterdam, 1961), p. 395.

    Google Scholar 

  15. A. N. Basu and S. Sengupta, Nuov. Cim. 106B, 511 (1991).

    ADS  Google Scholar 

  16. D. Bohm, Quantum Theory (Prentice Hall, Englewood Cliffs, NJ, 1951), Chap. 21.

    Google Scholar 

  17. A. Messiah, Quantum Mechanics, vol. 1 (North-Holland, Amsterdam, 1961), chap. 6.

    Google Scholar 

  18. M. Andrews, J. Phys. A. 14, 1123 (1981).

    Article  ADS  Google Scholar 

  19. A. Peres, Quantum Theory—Concepts and Methods (Kluwer, Dordrecht, Netherlands, 1993), chap. 10.

    MATH  Google Scholar 

  20. P. Holland, Quantum Theory of Motion (Cambridge Univer. Press, Cambridge, 1993), p. 256.

    Book  Google Scholar 

  21. L. E. Ballentine, Y. Gang, and J. P. Zibin, Phys. Rev. A 50, 2854 (1994).

    Article  ADS  Google Scholar 

  22. H. D. Zeh, Found Phys. 1, 69 (1970).

    Article  ADS  Google Scholar 

  23. W. H. Zurek, Phys. Today 44 (10), 36 (1991).

    Article  Google Scholar 

  24. Y. A. Kagan and A. J. Leggett, Quantum Tunnelling in Condensed Media (Else vier, Amsterdam, 1992), chap. 1.

    Google Scholar 

  25. A. J. Leggett, in Proc. 4th Int. Symp. on Foundations of Quantum Mechanics in the Light of New Technology (Japanese Journal of Applied Physics Publication, Tokyo, 1993), pp. 10–17.

    Google Scholar 

  26. E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985).

    Article  ADS  Google Scholar 

  27. R. Omnes, Interpretation of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1994), chap. 7.

    MATH  Google Scholar 

  28. H. Dekker, Phys. Rev. A 31, 1067 (1985).

    Article  ADS  Google Scholar 

  29. W. H. Zurek, in Frontiers of Nonequilibrium Statistical Physics (P. Mystre and M. O. Scully, eds.) (Plenum, New York, 1986) p. 145.

    Chapter  Google Scholar 

  30. W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  31. V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).

    Article  ADS  Google Scholar 

  32. W. H. Zurek, in Conceptual Problems of Quantum Gravity (A. Ashtekar and J. Stachel, eds.) (Birkhäuser, Boston, 1991), pp. 64–65.

    Google Scholar 

  33. R. P. Feynman and F. L. Vernon, Jr., Ann. Phys. (NY) 24, 118 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  34. A. O. Caldeira and A. J. Leggett, Ann. Phys. (NY) 149, 374 (1983).

    Article  ADS  Google Scholar 

  35. A. O. Caldeira and A. J. Leggett, Ann. Phys. (NY) 153, 445 (1984).

    Article  Google Scholar 

  36. G. S. Agarwal, Phys. Rev. A 4, 739 (1971).

    Article  ADS  Google Scholar 

  37. A. J. Leggett, in Chance and Matter (J. Souletie et al., eds.) (North-Holland, Amsterdam, 1987), pp. 411–416.

    Google Scholar 

  38. G. W. Ford, J. T. Lewis, and R. F. O Connell, Phys. Rev. A 37, 4419 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Venugopalan, Phys. Rev. A 50, 2742 (1994).

    Article  ADS  Google Scholar 

  40. W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  41. P. Pearle, True Collapse and False Collapse, Hamilton College Preprint (1995).

    Google Scholar 

  42. P. Holland, Quantum Theory of Motion (Cambridge Univer. Press, Cambridge, 1993), chap. 6.

    Book  Google Scholar 

  43. D. Home and S. Sengupta, Am. J. Phys. 51, 265 (1983).

    Article  ADS  Google Scholar 

  44. L. S. Brown, Am. J. Phys. 40, 371 (1972).

    Article  ADS  Google Scholar 

  45. P. Holland, in Bohmian Mechanics and Quantum Theory: An Appraisal (J. T. Cushing, A. Fine, and S. Goldstein, eds.) (Kluwer, Dordrecht, Netherlands, 1996), pp. 99–110.

    Chapter  Google Scholar 

  46. P. Holland, Found. Phys. Lett. 2, 471 (1989).

    Article  MathSciNet  Google Scholar 

  47. L. I. Schiff, Quantum Mechanics (McGraw-Hill, Tokyo, 1968), p. 76.

    Google Scholar 

  48. A. Einstein, in Scientific Papers Presented to Max Born (Oliver and Boyd, Edinburgh, Scotland, 1953), pp. 33–40.

    MATH  Google Scholar 

  49. D. Bohm, Scientific Papers Presented to Max Born (Oliver and Boyd, Edinburgh, Scotland, 1953), pp. 13–19.

    MATH  Google Scholar 

  50. D. Bohm and B. J. Hiley, Phys. Rev. Lett. 55, 2511 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  51. D. Bohm and B. J. Hiley, Undivided Universe (Routledge, London, 1993), chap. 8.

    Google Scholar 

  52. D. Bohm and B. J. Hiley, Undivided Universe (Routledge, London, 1993), pp. 115–16.

    Google Scholar 

  53. A. J. Leggett, in Percolation, Localization, and Superconductivity (A. M. Goldman and S. Wolf, eds.), NATO Advanced Study Institute, vol. 109 (Plenum, New York, 1984).

    Google Scholar 

  54. A. J. Leggett, in Directions in Condensed Matter Physics (G. Grinstein and G. Mazenko, eds.) (World Scientific, Singapore, 1986).

    Google Scholar 

  55. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).

    Article  ADS  Google Scholar 

  56. C. D. Tesche, J. R. Kirtley, W. J. Gallagher, A. W. Kleinsasser, R. L. Sandstrom, S. I. Raider, and M. P. A. Fisher, in Proc. 3rd Int. Symp. Foundations of Quantum Mechanics (S. Kobayashi et al., eds.) (Physical Society of Japan, Tokyo, 1989), pp. 233–43.

    Google Scholar 

  57. C. D. Tesche, Phys. Rev. Lett. 64, 2358 (1990).

    Article  ADS  Google Scholar 

  58. R. P. Feynman, R. B. Leighton, and M. Sands, Feynman Lectures on Physics, vol. 3 (Addison-Wesley, Reading, MA, 1964), chap. 9-1.

    Google Scholar 

  59. A. I. M. Rae, J. Phys. A 23, L57 (1990).

    Article  ADS  Google Scholar 

  60. M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990).

    Article  ADS  Google Scholar 

  61. A. J. Leggett, in Lesson of Quantum Theory (J. de Boer et al, eds.) (Elsevier, Amsterdam, 1986), p. 49.

    Google Scholar 

  62. A. J. Leggett, Prog. Theor. Phys. 69 (Suppl.), 80 (1980).

    Article  MathSciNet  Google Scholar 

  63. A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  64. A. J. Leggett, in Proc. 2d Int. Symp. on Foundations of Quantum Mechanics (M. Namiki et al., eds.) (Physical Society of Japan, Tokyo, 1987), p. 297.

    Google Scholar 

  65. D. W. Bol and R. de Bruyn Oubober, Physica 154B, 56 (1988).

    ADS  Google Scholar 

  66. R. K. Clifton, in Proceedings of the Symposium on the Foundations of Modern Physics 1990 (P. Lahti and P. Mittelstaedt, eds.) (World Scientific, Singapore, 1991).

    Google Scholar 

  67. M. Redhead, Incompleteness, Nonlocality, and Realism (Oxford Univer. Press, Oxford, UK, 1987), chap. 4.

    MATH  Google Scholar 

  68. S. Chakravarty and A. J. Leggett, Phys. Rev. Lett. 52, 5 (1984).

    Article  ADS  Google Scholar 

  69. A. J. Leggett, Found. Phys. 18, 939 (1988).

    Article  ADS  Google Scholar 

  70. L. Ballentine, Phys. Rev. Lett. 59, 1493 (1987).

    Article  ADS  Google Scholar 

  71. A. Peres, Phys. Rev. Lett. 61, 2019 (1987).

    Article  ADS  Google Scholar 

  72. A. J. Leggett and A. Garg, Phys. Rev. Lett. 59, 1621 (1987).

    Article  ADS  Google Scholar 

  73. S. Foster and A. Elby, Found. Phys. 21, 773 (1991).

    Article  ADS  Google Scholar 

  74. D. Home, in Bell’s Theorem and the Foundations of Modern Physics (A. Van der Merwe et al., eds.) (World Scientific, Singapore, 1992).

    Google Scholar 

  75. L. Hardy, D. Home, E. J. Squires, and M. A. B. Whitaker, Phys. Rev. A 45, 4267 (1992).

    Article  MathSciNet  ADS  Google Scholar 

  76. D. T. Gillespie, Phys. Lett. A 49, 1607 (1994).

    MathSciNet  Google Scholar 

  77. F. Benatti, G. C. Ghirardi, and R. Grassi, Found. Phys. Lett. 7, 105 (1994).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bose Institute, Calcutta, India

    Dipankar Home

Authors
  1. Dipankar Home
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Home, D. (1997). Classical Limit of Quantum Mechanics. In: Conceptual Foundations of Quantum Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9808-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9808-1_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9810-4

  • Online ISBN: 978-1-4757-9808-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation