Dynamical time versus system's time in quantum mechanics

doi:10.1088/1674-1056/21/7/070302

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70302-070302.doi: 10.1088/1674-1056/21/7/070302

Dynamical time versus system's time in quantum mechanics

Dušan Arsenović^a, Nikola Burić^a, Dragomir Davidović^b, Slobodan Prvanović^a

a Institute of Physics, University of Belgrade, P.O. Box 68, 11000 Belgrade, Serbia;
b Vinca Institute of Nuclear Sciences, P.O. Box 522, 11001 Belgrade, Serbia

收稿日期:2011-09-12 修回日期:2012-03-21 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
Project supported by the Ministry of Science and Education of the Republic of Serbia (Grant Nos. 171017, 171028, and 171006).

Dynamical time versus system's time in quantum mechanics

Duv san Arsenović^a), Nikola Burić^a)^†, Dragomir Davidović^b), and Slobodan Prvanović^a)

a Institute of Physics, University of Belgrade, P.O. Box 68, 11000 Belgrade, Serbia;
b Vinca Institute of Nuclear Sciences, P.O. Box 522, 11001 Belgrade, Serbia

Received:2011-09-12 Revised:2012-03-21 Online:2012-06-01 Published:2012-06-01
Contact: Nikola Burić E-mail:buric@ipb.ac.rs
Supported by:
Project supported by the Ministry of Science and Education of the Republic of Serbia (Grant Nos. 171017, 171028, and 171006).

摘要/Abstract

摘要： Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system's time operator, i.e., for the free one-dimensional particle, is obtained.

关键词: time operators, extended state space, positive operator valued measure

Abstract: Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system's time operator, i.e., for the free one-dimensional particle, is obtained.

Key words: time operators, extended state space, positive operator valued measure

中图分类号: (Formalism)

03.65.Ca

03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.65.Xp (Tunneling, traversal time, quantum Zeno dynamics)

Dušan Arsenović, Nikola Burić, Dragomir Davidović, Slobodan Prvanović. Dynamical time versus system's time in quantum mechanics[J]. 中国物理B, 2012, 21(7): 70302-070302.

Duv san Arsenović, Nikola Burić, Dragomir Davidović, and Slobodan Prvanović . Dynamical time versus system's time in quantum mechanics[J]. Chin. Phys. B, 2012, 21(7): 70302-070302.

参考文献 19

[1]	Dirac P A M 1930 Principles of Quantum Mechanics (Oxford: Claredon Press)
[2]	Ruffini G 2005 arXiv: 0511088 gr-qc
[3]	Macćias A and Quevedo H 2006 arXiv: 0610057 gr-qc
[4]	Kuchcheckar K V 1981 Canonical Methods of Quantization in Quantum Gravity (Oxford: Claredon Press)
[5]	Hanneaux M and Teitelboim 1992 Quantization of Gauge Systems (Princeton: Princeton Uni. Press)
[6]	Peres A 1997 arXiv: 97040 gr.qc
[7]	Aharonov Y and Bohm D 1961 Phys. Rev. 122 1649
[8]	Aharonov Y, Oppenheim J, Popescu S, Reznik B and Unruh W G 1998 Phys. Rev. A 57 4130
[9]	Muga J G, Sala Mayato R and Egusquiza I L 2001 Time in Quantum Mechanics (Berlin: Springer)
[10]	Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: Nort-Holland)
[11]	Busch P, Grabowski M and Lahti P J 1997 Operational Quantum Physics (2nd edn.) (Berlin: Springer)
[12]	Werner R 1987 Ann. Inst. Henri Poincare 47 429
[13]	Davidovic M 2003 Fortsch. der Physik 51 195
[14]	Lanczos C 1986 The Variational Principles of Mechanics (4th edn.) (New York: Dover Publication)
[15]	Kibble T W B 1979 Commun. Math. Phys. 65 189
[16]	Ashtekar A and Schilling T A 1998 Geometric Formulation of Quantum Mechanics in Einstein's Path (Berlin: Springer)
[17]	Brody D C and Hughston L P 2001 J. Phys. A 38 19
[18]	Burić N 2008 Ann. Phys. 233 17
[19]	Brody D C, Gustavsson A C T and Hughston L 2009 J. Phys. A 42 295303

Dynamical time versus system's time in quantum mechanics

Dynamical time versus system's time in quantum mechanics

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