Skip to main content
SpringerLink
Log in

From Weyl Expansion of Operator to Ordering of Operator and its New Applications

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge (1997)

  2. Fan, H.Y., Wang, T.T: Int. J. Theor. Phys. 48, 441 (2009)

    Article  MATH  Google Scholar 

  3. Fan, H.Y., Yuan, H.C., Jiang, N.Q.: Sci. China: Phys. Mech. Astron. 53, 1626 (2010)

    ADS  Google Scholar 

  4. Fan, H.Y.: Chin. Phys. B 19, 050303 (2010)

  5. Lee, H.W.: Phys. Rep. 259, 147 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  6. Fan, H.Y., Hu, L.Y., Yuan, H.C.: Chin. Phys. B 19, 060305 (2010)

    Article  ADS  Google Scholar 

  7. Fan, H.Y.: Sci. China: Phys. Mech. Astron. 55, 762 (2012)

    Article  ADS  Google Scholar 

  8. Hu, L.Y., Zhang, H.L., Jia, F., Tao, X.Y.: Chin. Phys. B 22, 120301 (2013)

    Article  Google Scholar 

  9. Hu, L.Y., Liu, S.Y., Zheng, K.M., Jia, F., Fan, H.Y.: Int. J. Theor. Phys. 53, 380 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  10. Marian, P., Marian, T.A.: Phys. Rev. A 74, 042306 (2006)

    Article  ADS  Google Scholar 

  11. Braunstein, S.L., Kimble, H.J.: Phys. Rev. Lett. 80, 869 (1998)

    Article  ADS  Google Scholar 

  12. Fan, H.Y.: Ann. Phys. 323, 500 (2008)

    Article  ADS  MATH  Google Scholar 

  13. Fan, H.Y.: J. Opt. B Quantum Semiclass Opt. 5, R147 (2003)

    Article  ADS  Google Scholar 

  14. Fan, H.Y.: Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific and Technical Publisher, 1997) (in Chinese) p. 27.

  15. Hu, L.Y., Xu, X.X., Guo, Q., Fan, H.Y.: Opt. Commun. 283, 5074 (2010)

    Article  ADS  Google Scholar 

  16. Loudon, R.: The Quantum Theory of Light. Oxford University Press, Oxford (1983)

    Google Scholar 

  17. Orszag, M.: Quantum Optics. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  18. Kelley, P.L., Kleiner, W.H.: Phys. Rev. 136, 316 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  19. Scully, M.O., Lamb, W.E.: Phys. Rev. 179, 368 (1969)

    Article  ADS  Google Scholar 

  20. Mollow, B.R.: Phys. Rev. 168, 1896 (1968)

    Article  ADS  Google Scholar 

  21. Fan, H.Y., Hu, L.Y.: Opt. Lett. 33, 443 (2008)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

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).

Author information

Authors and Affiliations

  1. Department of Material Science and Engineering, University of Science and Technology of China, Hefei, 230026, China

    Fang Jia & Hong-Yi Fan

  2. Key Laboratory of Optoelectronic and Telecommunication, Jiangxi Normal University, Nanchang, 330022, China

    Fang Jia, Hao-Liang Zhang & Li-Yun Hu

Authors
  1. Fang Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao-Liang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li-Yun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hong-Yi Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-Yun Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jia, F., Zhang, HL., Hu, LY. et al. From Weyl Expansion of Operator to Ordering of Operator and its New Applications. Int J Theor Phys 54, 1283–1291 (2015). https://doi.org/10.1007/s10773-014-2326-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2326-z

Keywords

Search

Navigation