Abstract
We examine the longstanding problem of introducing a time observable in quantum mechanics; using the formalism of positive-operator-valued measures, we show how to define such an observable in a natural way and we discuss some consequences.
Similar content being viewed by others
References
Aharonov, Y., and Bohm, D. (1961). Time in the quantum theory and the uncertainty relation for time and energy.Physical Review,122, 1649.
Blanchard, Ph., and Jadczyk, A. (1996). Time of events in quantum theory, Preprint quantph/9602010.
Bridgman, P. W. (1927).The Logic of Modern Physics, Macmillan, New York.
Busch, P., Lahti, P. J., and Mittelstaedt, P. (1991).The Quantum Theory of Measurement, Springer-Verlag, Berlin.
Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, London.
Giles, R. (1970). Foundations for quantum mechanics,Journal of Mathematical Physics,11, 2139.
Grot, N., Rovelli, C., and Tate, R. S. (1996). Time-of-arrival in quantum mechanics, Preprint quant-ph/9603021.
Ludwig, G. (1968). Attempt of an axiomatic foundation of quantum mechanics and more general theories III.Communications in Mathematical Physics,9, 1.
Mackey, G. W. (1963). Infinite dimensional group representations,Bulletin of the American Mathematical Society,69, 628.
Olkhovsky, V. S., Recami, E., and Gerasimchuk, A. J. (1974). Time operator in quantum mechanics. I: Nonrelativistic case,Nuovo Cimento,22, 263.
Pauli, W. (1958). Die allgemeinen Prinzipien der Wellenmechanik, inHandbuch der Physik, Vol. V/1, S. Flügge, ed., Springer-Verlag, Berlin, p. 60.
Prugovečki, E. (1971).Quantum Mechanics in Hilbert Space, Academic Press, New York.
Rosenbaum, D. M. (1969). Super Hilbert space and the quantum mechanical time operators,Journal of Mathematical Physics,10, 1127.
Titchmarsh, E. C. (1939).The Theory of Functions, Oxford University, Press, Oxford.
Toller, M. (1996). Quantum references and quantum transformations, Preprint gr-qc/9605052.
Varadarajan, V. S. (1984).Geometry of Quantum Theory, 2nd ed., Springer-Verlag, Berlin.
Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Giannitrapani, R. Positive-operator-valued time observable in quantum mechanics. Int J Theor Phys 36, 1575–1584 (1997). https://doi.org/10.1007/BF02435757
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02435757