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Chin. Phys. B, 2014, Vol. 23(3): 030305    DOI: 10.1088/1674-1056/23/3/030305
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Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators

Xu Xing-Leia b, Li Hong-Qia b, Fan Hong-Yic
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
Abstract  Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ωk(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 Ωk(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 Ωk(p,q) are also derived, which helps us to put the operators into their P- and Q- ordering, respectively.
Keywords:  generalized Wigner operator      generalized Weyl quantization scheme      different operator ordering rules      mutual transformation     
Received:  31 July 2013      Published:  15 March 2014
PACS:  03.65.-w (Quantum mechanics)  
  42.50.-p (Quantum optics)  
Fund: 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).
Corresponding Authors:  Xu Xing-Lei     E-mail:  xxlwlx@126.com

Cite this article: 

Xu Xing-Lei, Li Hong-Qi, Fan Hong-Yi Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators 2014 Chin. Phys. B 23 030305

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