|
|
|
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 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.
|
Received: 12 October 2015
Revised: 13 February 2016
Accepted manuscript online:
|
|
PACS:
|
03.65.-w
|
(Quantum mechanics)
|
| |
03.65.Db
|
(Functional analytical methods)
|
| |
03.65.Sq
|
(Semiclassical theories and applications)
|
| |
03.65.Ta
|
(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). |
Corresponding Authors:
Jeong Ryeol Choi
E-mail: choiardor@hanmail.net
|
Cite this article:
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
|
| [1] |
Maamache M and Bekkar H 2003 J. Phys. A:Math. Gen. 36 L359
|
| [2] |
Kim H C, Lee M H, Ji J Y and Kim J K 1996 Phys. Rev. A 53 3767
|
| [3] |
Abdalla M S and Choi J R 2007 Ann. Phys. 322 2795
|
| [4] |
de Lima A L, Rosas A and Pedrosa I A 2008 Ann. Phys. 323 2253
|
| [5] |
Planck M 1967 "The Genesis and Present State of Developement of the Quantum Theory", in Nobel Lectures:Physics 1901-1921 (Amsterdam:The Nobel Foundation)
|
| [6] |
Heilbron J L 2000 The Dilemmas of an Upright Man:Max Planck and the Fortunes of German Science (Cambridge:Harvard University Press), ISBN 0674004396
|
| [7] |
Pickover C 2008 Archimedes to Hawking:Laws of Sciences and Great Minds Behind Them (Oxford:Oxford University Press), ISBN 978-0195336115
|
| [8] |
Gamow G 1985 Thirty Years that Shook Physics:The Story of Quantum Theory (Dover:Dover Publications)
|
| [9] |
Ehrenfest P 1927 Zeits. f. Physik 45 455
|
| [10] |
Gao X C, Xu J B and Qian T Z 1990 Ann. Phys. 204 235
|
| [11] |
Yüce C 2003 Ann. Phys. 308 599
|
| [12] |
Colegrave R K and Abdalla M S 1981 Opt. Act. 28 495
|
| [13] |
Choi J R 2004 Int. J. Theor. Phys. 43 2113
|
| [14] |
Nassar A B 1984 Phys. Lett. A 106 43
|
| [15] |
Ge Y G and Child M S 1997 Phys. Rev. Lett. 78 2507
|
| [16] |
Ruark A E 1928 Phys. Rev. 31 533
|
| [17] |
Lewis H R Jr and Riesenfeld W B 1969 J. Math. Phys. 10 1458
|
| [18] |
Das R, Kumar S K K and Kumar A 2006 J. Magn. Reson. 177 318
|
| [19] |
Wu L A, Bishop C A and Byrd M S 2011 Phys. Rev. A 84 022341
|
| [20] |
Bekkar H, Benamira F and Maamache M 2003 Phys. Rev. A 68 016101
|
| [21] |
Maamache M, Saadi S, Choi J R and Yeon K H 2010 J. Korean Phys. Soc. 56 1063
|
| [22] |
Kälbermann G 2004 J. Phys. A:Math. Gen. 37 2999
|
| [23] |
Weinberg S 1989 Ann. Phys. 194 336
|
| [24] |
Jammer M 1966 The Conceptual Development of Quantum Mechanics (New York:Tomash Publishers)
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
