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

Salim Medjber^{1}, Hacene Bekkar^{2}, Salah Menouar^{3}, Jeong Ryeol Choi^{4}

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

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.

(Foundations of quantum mechanics; measurement theory)

Fund: 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).

Salim Medjber, Hacene Bekkar, Salah Menouar, Jeong Ryeol Choi Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola-Kanai oscillator driven by a time-dependent force 2016 Chin. Phys. B 25 080301

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