数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 795-808.

• 论文 • 上一篇    

关于厄米特多项式的新微分公式及其 在量子光学中的应用

孙云1, 吴建光1, 王东1, 唐绪兵1,2   

  1. 1. 安徽工业大学 数理科学与工程学院 安徽马鞍山 243032;
    2. 中科院合肥物质科学研究院智能所 合肥 230031
  • 收稿日期:2015-09-13 修回日期:2016-03-14 出版日期:2016-08-26 发布日期:2016-08-26
  • 通讯作者: 唐绪兵 E-mail:ttxxbb@ahut.edu.cn
  • 基金资助:

    国家自然科学基金(11204004,11574295,61374091)资助

New Differential Formulae Related to Hermite Polynomials and Their Applications in Quantum Optics

Sun Yun1, Wu Jianguang1, Wang Dong1, Tang Xubing1,2   

  1. 1. School of Mathematics and Physics Science and Engineering, Anhui University of Technology, Anhui Ma'anshan 243032;
    2. Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei 230031
  • Received:2015-09-13 Revised:2016-03-14 Online:2016-08-26 Published:2016-08-26
  • Supported by:

    Support by the NSFC(11204004,11574295,61374091)

摘要:

基于量子光学厄米特多项式和Weyl对应规则,该文给出了一类双变量厄米特多项式的生成函数. 考虑到Weyl编序的相似变换不变性特征,还得到了另一个厄米特多项式广义生成函数,这些生成函数能被用于研究量子光场的非经典特征.

关键词: Weyl对应规则, 厄米特多项式, 相似变换

Abstract:

In this work, based on quantum operator Hermite polynomials and Weyl's mapping rule, we find a generation function of the two-variable Hermite polynomials. And then, noting that the Weyl ordering is invariant under the similar transformations, we obtain another generalized differential expression related to the Hermite polynomials. Those identites can be applied to investigate the nonclasscial properties of quantum optical fields.

Key words: Weyl mapping rule, Hermite polynomials, Similar transformation

中图分类号: 

  • O174.14