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Communications in Theoretical Physics

Normally Ordered Form of Smoothed Wigner Operator and its Applications

Hong-Yi Fan, Guo-Liang Tong

Published Apr 1, 1989• 3 citations
Publisher

Abstract

Using the IWOP (integration within ordered product) technique, we derive a normally ordered form of the smoothed Wigner operator with which the smoothed Wigner function, that is specified only in the integral form in the literature, can be simplified. The application of the new form of the smoothed Wigner operator to the coherent state is also presented.

DOI
10.1088/0253-6102/11/3/291

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Using the IWOP (integration within ordered product) technique, we derive a normally ordered form of the smoothed Wigner operator with which the smoothed Wigner function, that is specified only in the integral form in the literature, can be simplified. The application of the new form of the smoothed Wigner operator to the coherent state is also presented.
We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also