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Chin. Phys. B, 2020, Vol. 29(10): 100301    DOI: 10.1088/1674-1056/ab99aa
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Ordered product expansions of operators (AB)±m with arbitrary positive integer

Shi-Min Xu(徐世民)1, Yu-Shan Li(李玉山)1, Xing-Lei Xu(徐兴磊)1,†, Lei Wang(王磊)1,2,‡, and Ji-Suo Wang(王继锁)2
1 College of Physics and Electronic Engineering, Heze University, Heze 274015, China
2 College of Physics and Engineering, Qufu Normal University, Qufu 273165, China
Abstract  

We arrange quantum mechanical operators (a a)m in their normally ordered product forms by using Touchard polynomials. Moreover, we derive the anti-normally ordered forms of (a a)± m by using special functions as well as Stirling-like numbers together with the general mutual transformation rule between normal and anti-normal orderings of operators. Further, the ℚ- and ℙ-ordered forms of (QP)±m are also obtained by using an analogy method.

Keywords:  Fock space      new polynomial      ordered product      analogy method  
Received:  15 March 2020      Revised:  12 May 2020      Accepted manuscript online:  05 June 2020
PACS:  03.65.-w (Quantum mechanics)  
  03.67.-a (Quantum information)  
  89.70.-a (Information and communication theory)  
Corresponding Authors:  Corresponding author. E-mail: xxlwlx@126.com Corresponding author. E-mail: wanglei1692@163.com   
About author: 
†Corresponding author. E-mail: xxlwlx@126.com
‡Corresponding author. E-mail: wanglei1692@163.com
* Project supported by the National Natural Science Foundation of China (Grant No. 11804085) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2017MEM012).

Cite this article: 

Shi-Min Xu(徐世民), Yu-Shan Li(李玉山), Xing-Lei Xu(徐兴磊)†, Lei Wang(王磊)‡, and Ji-Suo Wang(王继锁) Ordered product expansions of operators (AB)±m with arbitrary positive integer 2020 Chin. Phys. B 29 100301

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