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Uncertainties and an interpretation of nonrelativistic quantum theory


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 · Δpħ/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.

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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Ishikawa, S. Uncertainties and an interpretation of nonrelativistic quantum theory. Int J Theor Phys 30, 401–417 (1991).

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  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Quantum Mechanic
  • Quantum Theory