中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1534-1541.doi: 10.1088/1674-1056/18/4/040

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Normal ordering and antinormal ordering of the operator ( fQ+gP)n and some of their applications

孟祥国, 王继锁, 梁宝龙   

  1. Department of Physics, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2008-09-24 修回日期:2008-10-13 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    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).

Normal ordering and antinormal ordering of the operator $(fQ+gP)^n$ and some of their applications

Meng Xiang-Guo(孟祥国)†, Wang Ji-Suo(王继锁), and Liang Bao-Long(梁宝龙)   

  1. Department of Physics, Liaocheng University, Liaocheng 252059, China
  • Received:2008-09-24 Revised:2008-10-13 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    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).

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摘要： 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.

关键词: normal ordering, antinormal ordering, IWOP technique, intermediate coordinate-momentum representation

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.

Key words: normal ordering, antinormal ordering, IWOP technique, intermediate coordinate-momentum representation

中图分类号:  (Quantum optics)

  • 42.50.-p
03.65.Fd (Algebraic methods) 02.30.Tb (Operator theory)