By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving mis...By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.展开更多
By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner ...By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator （pure state）, which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.展开更多
文摘By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.
基金Supported by National Natural Science Foundation of China under Grant No.10874174
文摘By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator （pure state）, which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.
