|
|
|
New approach to Q-P (P-Q) ordering of quantum mechanical operators and its applications |
| Hu Li-Yun (胡利云), Zhang Hao-Liang (张浩亮), Jia Fang (贾芳), Tao Xiang-Yang (陶向阳) |
| Center for Quantum Science and Technology, College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China |
|
|
|
|
Abstract In this paper, we introduce a new way to obtain the Q-P (P-Q) ordering of quantum mechanical operators, i.e., from the classical correspondence of Q-P (P-Q) ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single (two-) mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator’s Q-P (P-Q) ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q-P ordering of operators.
|
Received: 03 April 2013
Revised: 08 May 2013
Accepted manuscript online:
|
|
PACS:
|
03.65.Ca
|
(Formalism)
|
| |
02.90.+p
|
(Other topics in mathematical methods in physics)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11264018), the Natural Science Foundation of Jiangxi Province of China (Grant No. 20132BAB212006), and the Fund from the Key Laboratory of Optoelectronics and Telecommunication of Jiangxi Province, China. |
Corresponding Authors:
Hu Li-Yun
E-mail: hlyun@jxnu.edu.cn
|
Cite this article:
Hu Li-Yun (胡利云), Zhang Hao-Liang (张浩亮), Jia Fang (贾芳), Tao Xiang-Yang (陶向阳) New approach to Q-P (P-Q) ordering of quantum mechanical operators and its applications 2013 Chin. Phys. B 22 120301
|
| [1] |
Dirac P A M 1958 The Principle of Quantum Mechanics, 4th edn. (Oxford: Oxford University Press)
|
| [2] |
Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
|
| [3] |
Fan H Y 2008 Ann. Phys. 323 500
|
| [4] |
Fan H Y 2010 Chin. Phys. B 19 040305
|
| [5] |
Lee H W 1995 Phys. Rep. 259 147
|
| [6] |
Balazs N L and Jenning B K 1984 Phys. Rep. 104 347
|
| [7] |
Wang J S, Fan H Y and Meng X G 2012 Chin. Phys. B 21 064204
|
| [8] |
Fan H Y 2012 Sci. China: Phys. Mech. Astron. 55 762
|
| [9] |
Louisell W H 1973 Quantum Statistical Properties of Radiation (New York: John Wiley)
|
| [10] |
Puri R R 2001 Mathematical Methods of Quantum Optics (Berline: Springer-Verlag), Appendix A
|
| [11] |
Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics: Progress of Dirac’s Symbolic Method (Shanghai: Shanghai Scientific & Technical Publishers)
|
| [12] |
Fan H Y and Hu L Y 2012 Front. Phys. 7 261
|
| [13] |
Loudon R 1983 The Quantum Theory of Light (Oxford: Oxford University Press)
|
| [14] |
Orszag M 2000 Quantum Optics (Berlin: Springer)
|
| [15] |
Fan H Y and Hu L Y 2008 Opt. Lett. 33 443
|
| [16] |
Hu L Y, Wang Z S, Kwek L C and Fan H Y 2011 Chin. Phys. B 20 084203
|
| [17] |
Hu L Y, Xu X X, Wang Z S and Xu X F 2010 Phys. Rev. A 82 043842
|
| 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
|
|
|
