Abstract In this paper by virtue of the technique of integration within an ordered product (IWOP) of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator $(fQ+gP)^n$ when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given.
Received: 24 September 2008
Revised: 13 October 2008
Accepted manuscript online:
Fund: Project
supported by the Natural Science Foundation of Shandong Province of
China (Grant No Y2008A23) and the Natural Science Foundation of
Liaocheng University (Grant No X071049).
Cite this article:
Meng Xiang-Guo(孟祥国), Wang Ji-Suo(王继锁), and Liang Bao-Long(梁宝龙) Normal ordering and antinormal ordering of the operator $(fQ+gP)^n$ and some of their applications 2009 Chin. Phys. B 18 1534
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