Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendr...Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.展开更多
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...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 ofΩs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics.Three different expressions ofΩs and the quantization scheme with use of it are presented.展开更多
文摘Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.
基金Supported by the National Natural Science Foundation of China under Grant No.10574060the Natural Science Foundation of Shandong Province under Grant No.ZR2010AQ027the Shandong Provincial Higher Educational Science and Technology Program under Grant Nos.J09LA07 and J10LA15.
文摘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 ofΩs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics.Three different expressions ofΩs and the quantization scheme with use of it are presented.
