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Prog. Theor. Phys. Vol. 64 No. 1 (1980) pp. 1-17
The Time as an Observable in Quantum Mechanics
Tetsuo Gotō,
Shigefumi Naka and
Katsuhito Yamaguchi
Atomic Energy Research Institute, College of Science and Technology, Nihon University, Tokyo 101
(Received February 16, 1980)
Abstract:
Following homogeneous canonical formalism where the time is treated on an equal footing with the space coordinates, we propose an alternative formulation of quantum mechanics in which the time is considered as a dynamical variable. The basic equation corresponding to and being equivalent to the ordinary Schrödinger equation is obtained when we consider the space coordinates x as a parameter corresponding to the time t in the ordinary formulation. The formal solution of this equation is given and examined. By making use of this solution the scattering theory is formulated in our formalism.
It is shown that observables corresponding to the time and space coordinates can be defined. A short comment on the energy-time uncertainty relation is also given.
URL :
http://ptp.ipap.jp/link?PTP/64/1/
DOI : 10.1143/PTP.64.1
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1525-1538
:
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On the Time Operator in Quantum Mechanics
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Tetsuo Gotō, Katsuhito Yamaguchi and Naoshi Sudō
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Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 1915-1925
:
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On the Time Operator in Quantum Mechanics. II
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Tetsuo Gotō, Shigefumi Naka and Katsuhito Yamaguchi
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Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 158-170
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Time Compound Nucleus for High Energy Nuclear Reactions
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Ko Izumo and Hitoshi Araseki
