Skip to main content
SpringerLink
Log in

Uncertainties and an interpretation of nonrelativistic quantum theory

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We propose an interpretation of nonrelativistic quantum theory which can be considered a generalized Copenhagen interpretation. The uncertainties (i.e., Δq and Δp) in Heisenberg's uncertainty relation Δq · Δp≥ħ/2 can be characterized as (average) errors in an approximate simultaneous measurement if the interpretation proposed here is accepted in nonrelativistic quantum mechanics. Under this interpretation, the (discrete) trajectory of a particle (like “Wilson chamber”) is significant enough. We propose to analyze this trajectory numerically.

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

  • Abu-Zeid, O. (1987).Physics Letters A,125, 162–164.

    Google Scholar 

  • Ali, S. T., and Emch, G. G. (1974).Journal of Mathematical Physics,15(2), 176–182.

    Google Scholar 

  • Ali, S. T., and Prugovečki, E. (1976).Journal of Mathematical Physics,18(2), 219–228.

    Google Scholar 

  • Arthurs, E., and Kelly, J. L., Jr. (1965).Bell System Technical Journal,44, 725–729.

    Google Scholar 

  • Ash, B. R. (1972).Real Analysis and Probability, Academic Press, New York.

    Google Scholar 

  • Busch, P. (1985).International Journal of Theoretical Physics,24, 63–92.

    Google Scholar 

  • Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, New York.

    Google Scholar 

  • Einstein, A., Podolsky, B., and Rosen, N. (1935).Physical Review,47, 777–780.

    Google Scholar 

  • Holevo, A. S. (1982).Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam.

    Google Scholar 

  • Ishikawa, S. (1991). Uncertainty relations in simultaneous measurements for arbitrary observables,Reports on Mathematical Physics, to appear.

  • Prugovečki, E. (1981).Quantum Mechanics in Hilbert Space, Academic Press, New York.

    Google Scholar 

  • Selleri, F. (1990).Quantum Paradoxes and Physical Reality, Kluwer Academic Publishers.

  • She, C. Y., and Heffner, H. (1966).Physical Review,152, 1103–1110.

    Google Scholar 

  • Von Neumann, J. (1932).Die Mathematische Grundlagen Der Quantenmechanik, Springer-Verlag, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, 223, Yokohama, Japan

    Shiro Ishikawa

Authors
  1. Shiro Ishikawa
    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

Ishikawa, S. Uncertainties and an interpretation of nonrelativistic quantum theory. Int J Theor Phys 30, 401–417 (1991). https://doi.org/10.1007/BF00672888

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00672888

Keywords

Search

Navigation