中国物理B ›› 2014, Vol. 23 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/23/6/060301

• GENERAL • 上一篇    下一篇

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

范洪义, 展德会   

  1. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2013-11-04 修回日期:2013-12-05 出版日期:2014-06-15 发布日期:2014-06-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

Fan Hong-Yi (范洪义), Zhan De-Hui (展德会)   

  1. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2013-11-04 Revised:2013-12-05 Online:2014-06-15 Published:2014-06-15
  • Contact: Zhan De-Hui E-mail:dhzhan@mail.ustc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).

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摘要： By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

关键词: generating function, even- and odd-Hermite polynomials, Hermite polynomial method, technique of integral within an ordered product of operators

Abstract: By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

Key words: generating function, even- and odd-Hermite polynomials, Hermite polynomial method, technique of integral within an ordered product of operators

中图分类号: 

  • 03.65.-a
02.30.Gp (Special functions)