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, access via your institution.
References
Abu-Zeid, O. (1987).Physics Letters A,125, 162–164.
Ali, S. T., and Emch, G. G. (1974).Journal of Mathematical Physics,15(2), 176–182.
Ali, S. T., and Prugovečki, E. (1976).Journal of Mathematical Physics,18(2), 219–228.
Arthurs, E., and Kelly, J. L., Jr. (1965).Bell System Technical Journal,44, 725–729.
Ash, B. R. (1972).Real Analysis and Probability, Academic Press, New York.
Busch, P. (1985).International Journal of Theoretical Physics,24, 63–92.
Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, New York.
Einstein, A., Podolsky, B., and Rosen, N. (1935).Physical Review,47, 777–780.
Holevo, A. S. (1982).Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam.
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.
Selleri, F. (1990).Quantum Paradoxes and Physical Reality, Kluwer Academic Publishers.
She, C. Y., and Heffner, H. (1966).Physical Review,152, 1103–1110.
Von Neumann, J. (1932).Die Mathematische Grundlagen Der Quantenmechanik, Springer-Verlag, Berlin.
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00672888
Keywords
- Field Theory
- Elementary Particle
- Quantum Field Theory
- Quantum Mechanic
- Quantum Theory