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

作　　者：胡利云 张浩亮 贾芳 陶向阳 

机构地区：[1]Center for Quantum Science and Technology, College of Physics and Communication Electronics, Jiangxi Normal University

出　　处：《Chinese Physics B》2013年第12期70-73,共4页中国物理B（英文版）

基　　金：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);the Fund from the Key Laboratory of Optoelectronics and Telecommunication of Jiangxi Province,China

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.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 

分 类 号：O413.1[理学—理论物理] O223[理学—物理]