A generalized Weyl-Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators  

作　　者：王继锁 范洪义 孟祥国 

机构地区：[1]Shandong Provincial Key Laboratory of Laser Polarization and Information Technology,College of Physics and Engineering,Qufu Normal University [2]Department of Physics,Liaocheng University [3]Department of Physics,Shanghai Jiao Tong University

出　　处：《Chinese Physics B》2012年第6期207-212,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009);the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027);the Program of Higher Educational Science and Technology of Shandong Province,China (Grant No. J10LA15)

摘　　要：By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.

关 键 词：generalized Wigner operator generalized operator ordering rule bivariate normal dis-tribution 

分 类 号：O431.2[机械工程—光学工程]