| New approach to Q-P （P-Q） ordering of quantum mechanical operators and its applications |
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| 引用本文： | 胡利云,张浩亮,贾芳,陶向阳.New approach to Q-P （P-Q） ordering of quantum mechanical operators and its applications[J].中国物理 B,2013(12):70-73. |
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| 作者姓名： | 胡利云 张浩亮 贾芳 陶向阳 |
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| 作者单位： | Center for Quantum Science and Technology, College of Physics and Communication Electronics, ]iangxi Normal University, Nanchang 330022, China, College of Physics and Communication Electronics, ]iangxi Normal University, Nanchang 330022, China |
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| 基金项目： | 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 |
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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.
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| 关 键 词： | 量子力学 运营商 排序 应用 动量算符 双模压缩 计数公式 经营者 |
New approach to Q-P (P-Q) ordering of quantum mechanical operators and its applications |
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| Hu Li-Yun,Zhang Hao-Liang,Jia Fang,Tao Xiang-Yang.New approach to Q-P (P-Q) ordering of quantum mechanical operators and its applications[J].Chinese Physics B,2013(12):70-73. |
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| Authors: | Hu Li-Yun Zhang Hao-Liang Jia Fang Tao Xiang-Yang |
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| 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. |
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| Keywords: | Q-P(P-Q) ordering Fresnel operator photo-counting |
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