中国物理B ›› 2014, Vol. 23 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/23/12/120301

• GENERAL • 上一篇    下一篇

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

展德会a b, 范洪义a   

  1. a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
    b College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China
  • 收稿日期:2014-04-01 修回日期:2014-06-23 出版日期:2014-12-15 发布日期:2014-12-15
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grnat No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

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

  1. a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
    b College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China
  • Received:2014-04-01 Revised:2014-06-23 Online:2014-12-15 Published:2014-12-15
  • Contact: Zhan De-Hui E-mail:dhzhan@mail.ustc.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grnat No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).

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摘要：

We derive some new generating function formulae of the two-variable Hermite polynomials, such as ???140785-01???, ???140785-02???, and ???140785-03???. We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

关键词: generating function, two-variable Hermite polynomials, Hermite polynomial method, technique of integral within an ordered product of operators

Abstract:

We derive some new generating function formulae of the two-variable Hermite polynomials, such as , , and . We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

Key words: generating function, two-variable Hermite polynomials, Hermite polynomial method, technique of integral within an ordered product of operators

中图分类号:  (Quantum mechanics)

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