中国物理B ›› 2016, Vol. 25 ›› Issue (8): 80303-080303.doi: 10.1088/1674-1056/25/8/080303

• GENERAL • 上一篇    下一篇

New useful special function in quantum optics theory

Feng Chen(陈锋), Hong-Yi Fan(范洪义)   

  1. 1 Department of Mathematics and Physics, Hefei University, Hefei 230601, China;
    2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2016-02-16 修回日期:2016-04-06 出版日期:2016-08-05 发布日期:2016-08-05
  • 通讯作者: Feng Chen E-mail:chenfeng@hfuu.edu.cn
  • 基金资助:

    Project supported by the Natural Science Fund of Education Department of Anhui Province, China (Grant No. KJ2016A590), the Talent Foundation of Hefei University, China (Grant No. 15RC11), and the National Natural Science Foundation of China (Grant Nos. 11247009 and 11574295).

New useful special function in quantum optics theory

Feng Chen(陈锋)1, Hong-Yi Fan(范洪义)2   

  1. 1 Department of Mathematics and Physics, Hefei University, Hefei 230601, China;
    2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2016-02-16 Revised:2016-04-06 Online:2016-08-05 Published:2016-08-05
  • Contact: Feng Chen E-mail:chenfeng@hfuu.edu.cn
  • Supported by:

    Project supported by the Natural Science Fund of Education Department of Anhui Province, China (Grant No. KJ2016A590), the Talent Foundation of Hefei University, China (Grant No. 15RC11), and the National Natural Science Foundation of China (Grant Nos. 11247009 and 11574295).

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摘要：

By virtue of the operator Hermite polynomial method[Fan H Y and Zhan D H 2014Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involving both power-series and Hermite polynomials, i.e.,
??? (n!m!(-1)l/l!(n-l)!(m-l)!)Hn-l(x)ym-l≡ϑn, m(x, y).
By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

关键词: Hermite polynomial excitation state, IWOP method, new special function, generating function, operator Hermite polynomial method

Abstract:

By virtue of the operator Hermite polynomial method[Fan H Y and Zhan D H 2014Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involving both power-series and Hermite polynomials, i.e.,
(n!m!(-1)l/l!(n-l)!(m-l)!)Hn-l(x)ym-l≡ϑn, m(x, y).
By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

Key words: Hermite polynomial excitation state, IWOP method, new special function, generating function, operator Hermite polynomial method

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics)