Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

doi:10.1088/1674-1056/23/3/030305

中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30305-030305.doi: 10.1088/1674-1056/23/3/030305

Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

徐兴磊^{a b}, 李洪奇^{a b}, 范洪义^c

a Department of Physics, Heze University, Heze 274015, China;
b Key Laboratory of Quantum Communication and Calculation, Heze University, Heze 274015, China;
c Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

收稿日期:2013-07-31 修回日期:2013-08-27 出版日期:2014-03-15 发布日期:2014-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11175113), the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16), the University Experimental Technology Foundation of Shandong Province of China (Grant No. S04W138), and the Natural Science Foundation of Heze University of Shandong Province of China (Grants Nos. XY07WL01 and XY08WL03).

Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

Xu Xing-Lei (徐兴磊)^{a b}, Li Hong-Qi (李洪奇)^{a b}, Fan Hong-Yi (范洪义)^c

a Department of Physics, Heze University, Heze 274015, China;
b Key Laboratory of Quantum Communication and Calculation, Heze University, Heze 274015, China;
c Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Received:2013-07-31 Revised:2013-08-27 Online:2014-03-15 Published:2014-03-15
Contact: Xu Xing-Lei E-mail:xxlwlx@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11175113), the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16), the University Experimental Technology Foundation of Shandong Province of China (Grant No. S04W138), and the Natural Science Foundation of Heze University of Shandong Province of China (Grants Nos. XY07WL01 and XY08WL03).

摘要/Abstract

摘要： Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ω_k(p,q) with a real k parameter and can unify the P–Q, Q–P, and Weyl ordering of operators in k=1,-1,0, respectively, we find the mutual transformations between δ(p-P)δ(q-Q), δ(q-Q)δ(p-P), and Ω_k(p,q), which are, respectively, the integration kernels of the P–Q, Q–P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The P- and Q- ordered forms of Ω_k(p,q) are also derived, which helps us to put the operators into their P- and Q- ordering, respectively.

关键词: generalized Wigner operator, generalized Weyl quantization scheme, different operator ordering rules, mutual transformation

Abstract: Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ω_k(p,q) with a real k parameter and can unify the P–Q, Q–P, and Weyl ordering of operators in k=1,-1,0, respectively, we find the mutual transformations between δ(p-P)δ(q-Q), δ(q-Q)δ(p-P), and Ω_k(p,q), which are, respectively, the integration kernels of the P–Q, Q–P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The P- and Q- ordered forms of Ω_k(p,q) are also derived, which helps us to put the operators into their P- and Q- ordering, respectively.

Key words: generalized Wigner operator, generalized Weyl quantization scheme, different operator ordering rules, mutual transformation

中图分类号: (Quantum mechanics)

03.65.-w

42.50.-p (Quantum optics)

徐兴磊, 李洪奇, 范洪义. Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators[J]. 中国物理B, 2014, 23(3): 30305-030305.

Xu Xing-Lei (徐兴磊), Li Hong-Qi (李洪奇), Fan Hong-Yi (范洪义). Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators[J]. Chin. Phys. B, 2014, 23(3): 30305-030305.

参考文献 14

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[3]	Li X C, Yang Y and Fan H Y 2013 Acta Phys. Sin. 62 080301 (in Chinese)
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[6]	See E G and Schleich W P 2001 Quantum Optics in Phase Space (Berlin: Wiley-VCH)
[7]	Hu L Y and Fan H Y 2009 Phys. Rev. A 80 022115
[8]	Wang J S, Fan H Y and Meng X G 2012 Chin. Phys. B 21 064204
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[10]	Fan H Y and Zaidi H 1987 Phys. Lett. A 124 303
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[12]	Fan H Y and Yang Y L 2006 Phys. Lett. A 353 439
[13]	Fan H Y 1992 J. Phys. A 25 3443
[14]	Fan H Y 2008 Ann. Phys. 323 1502

Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

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