Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/22/12/120301

• GENERAL • 上一篇    下一篇

New approach to Q-P (P-Q) ordering of quantum mechanical operators and its applications

胡利云, 张浩亮, 贾芳, 陶向阳   

  1. Center for Quantum Science and Technology, College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
  • 收稿日期:2013-04-03 修回日期:2013-05-08 出版日期:2013-10-25 发布日期:2013-10-25
  • 基金资助:
    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.

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)   

  1. Center for Quantum Science and Technology, College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
  • Received:2013-04-03 Revised:2013-05-08 Online:2013-10-25 Published:2013-10-25
  • Contact: Hu Li-Yun E-mail:hlyun@jxnu.edu.cn
  • Supported by:
    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.

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摘要： 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.

关键词: Q-P (P-Q) ordering, Fresnel operator, photo-counting

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.

Key words: Q-P (P-Q) ordering, Fresnel operator, photo-counting

中图分类号:  (Formalism)

  • 03.65.Ca
02.90.+p (Other topics in mathematical methods in physics)