Weyl Operators

RL Hudson, Kalyanapuram Rangachari Parthasarathy

Fan Hong-Yi

The Moyal bracket is an exemplification of Weyl's correspondence to formulate quantum mechancis in terms of Wigner function. Here we present a formalism of Weyl-ordered operator Moyal bracket by virtue of the method of integral within a Weyl ordered product of operators and the Weyl ordering operator formula.

Wong, M W

Hong-Yi Fan, Hai-Guang Weng

A Weyl ordering product operation (with its representative symbol) is introduced. On the basis of the operation, a technique of integration within a Weyl ordered product is put forward. Application of the technique to the coherent state representation leads us to derive the Weyl ordered forms of some important operators in quantum mechanics, which can be rigorously checked by the relation between our Weyl ordering product operation and the Weyl correspondence rule.

Leon W. Cohen

Hong-Yi Fan, Yue Fan

We derive a new Weyl ordering operator formula which recasts given operators into Weyl ordering. In so doing, the Weyl ordering formulation of the entangled state representation is obtained, which turns out to be the Weyl ordered Dirac δ-operator functions. The Weyl ordering of the Wigner operator and squeezing operator in entangled state representation are also deduced.