From Weyl Expansion of Operator to Ordering of Operator and its New Applications
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By using the IWOP technique, Weyl expansion of operator is derived. Based on this, three new ordering formulas of operators are presented, which have been applied to calculate Q-P and P-Q ordering of some operators. As other applications of Weyl expansion, the formula of photon counting is also easily obtained, which are related to Wigner and Q-function. In particular, noticing the Weyl ordering of displacement operator is itself, Weyl ordering invariance under similarity transformations is conveniently proved, instead of using of Wigner operator.
KeywordsWeyl expansion Operator ordering Photon counting Weyl ordering invariance
Project supported by the National Natural Science Foundation of China (Grant No. 11264018), the Natural Science Foundation of Jiangxi Province of China (Grant No. 20132BAB212006), and the Research Foundation of the Education Department of Jiangxi Province of China (no GJJ14274) as well as Degree and postgraduate education teaching reform project of jiangxi province(No. JXYJG-2013-027).
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