Ordered product expansions of operators (AB)±m with arbitrary positive integer

doi:10.1088/1674-1056/ab99aa

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).

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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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Ordered product expansions of operators (AB)^±m with arbitrary positive integer