A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution
WANG Ji-Suo1,2**, MENG Xiang-Guo2, FAN Hong-Yi2
1Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165 2Department of Physics, Liaocheng University, Liaocheng 252059
A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution
WANG Ji-Suo1,2**, MENG Xiang-Guo2, FAN Hong-Yi2
1Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165 2Department of Physics, Liaocheng University, Liaocheng 252059
摘要By extending the usual Wigner operator to the s−parameterized one, we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P. This can be exposed by comparing the normally ordered form of Ωs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics. Three different expressions of Ωs and the quantization scheme with use of it are presented.
Abstract：By extending the usual Wigner operator to the s−parameterized one, we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P. This can be exposed by comparing the normally ordered form of Ωs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics. Three different expressions of Ωs and the quantization scheme with use of it are presented.
WANG Ji-Suo;**;MENG Xiang-Guo;FAN Hong-Yi
. A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution[J]. 中国物理快报, 2011, 28(10): 104209-104209.
WANG Ji-Suo, **, MENG Xiang-Guo, FAN Hong-Yi
. A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution. Chin. Phys. Lett., 2011, 28(10): 104209-104209.
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2011, Vol. 28 
