中国物理B ›› 2016, Vol. 25 ›› Issue (8): 80301-080301.doi: 10.1088/1674-1056/25/8/080301

• GENERAL •    下一篇

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola-Kanai oscillator driven by a time-dependent force

Salim Medjber, Hacene Bekkar, Salah Menouar, Jeong Ryeol Choi   

  1. 1 Department of Material Science, Faculty of Science, University of M'sila, M'sila, 28000, Algeria;
    2 Faculty of Technology, University of Ferhat Abbas Setif 1, Setif 19000, Algeria;
    3 Laboratory of Optoelectronics and Compounds(LOC), Department of Physics, Faculty of Science, University of Ferhat Abbas Setif 1, Setif 19000, Algeria;
    4 Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Republic of Korea
  • 收稿日期:2015-10-12 修回日期:2016-02-13 出版日期:2016-08-05 发布日期:2016-08-05
  • 通讯作者: Jeong Ryeol Choi E-mail:choiardor@hanmail.net
  • 基金资助:
    Project supported by Fund from the Algerian Ministry of Higher Education and Scientific Research (Grant No. CNEPRU/D01220120010) and the Basic Science Research Program of the year 2015 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. NRF-2013R1A1A2062907).

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola-Kanai oscillator driven by a time-dependent force

Salim Medjber1, Hacene Bekkar2, Salah Menouar3, Jeong Ryeol Choi4   

  1. 1 Department of Material Science, Faculty of Science, University of M'sila, M'sila, 28000, Algeria;
    2 Faculty of Technology, University of Ferhat Abbas Setif 1, Setif 19000, Algeria;
    3 Laboratory of Optoelectronics and Compounds(LOC), Department of Physics, Faculty of Science, University of Ferhat Abbas Setif 1, Setif 19000, Algeria;
    4 Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Republic of Korea
  • Received:2015-10-12 Revised:2016-02-13 Online:2016-08-05 Published:2016-08-05
  • Contact: Jeong Ryeol Choi E-mail:choiardor@hanmail.net
  • Supported by:
    Project supported by Fund from the Algerian Ministry of Higher Education and Scientific Research (Grant No. CNEPRU/D01220120010) and the Basic Science Research Program of the year 2015 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. NRF-2013R1A1A2062907).

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摘要： The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schrödinger equation for the Caldirola-Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular, we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.

关键词: Ehrenfest theorem, time-dependent Hamiltonian system, invariant theory

Abstract: The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schrödinger equation for the Caldirola-Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular, we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.

Key words: Ehrenfest theorem, time-dependent Hamiltonian system, invariant theory

中图分类号:  (Quantum mechanics)

  • 03.65.-w
03.65.Db (Functional analytical methods) 03.65.Sq (Semiclassical theories and applications) 03.65.Ta (Foundations of quantum mechanics; measurement theory)