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

作　　者：徐兴磊 李洪奇 范洪义 

机构地区：[1]Department of Physics, Heze University [2]Key Laboratory of Quantum Communication and Calculation, Heze University [3]Department of Material Science and Engineering, University of Science and Technology of China

出　　处：《Chinese Physics B》2014年第3期119-122,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.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);the Natural Science Foundation of Heze University of Shandong Province of China(Grants Nos.XY07WL01 and XY08WL03)

摘　　要：Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （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 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （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 - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （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 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （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 - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.

关 键 词：generalized Wigner operator generalized Weyl quantization scheme different operator orderingrules mutual transformation 

分 类 号：O413[理学—理论物理]