Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (4): 795-808.

Previous Articles    

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)

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

CLC Number: 

  • O174.14
Trendmd