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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 |
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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.
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Received: 31 July 2013
Revised: 27 August 2013
Accepted manuscript online:
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PACS:
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03.65.-w
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(Quantum mechanics)
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42.50.-p
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(Quantum optics)
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| 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
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Cite this article:
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 2014 Chin. Phys. B 23 030305
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