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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 |
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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.
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Received: 15 March 2020
Revised: 12 May 2020
Accepted manuscript online: 05 June 2020
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PACS:
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03.65.-w
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(Quantum mechanics)
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03.67.-a
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(Quantum information)
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89.70.-a
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(Information and communication theory)
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Corresponding Authors:
†Corresponding author. E-mail: xxlwlx@126.com ‡Corresponding author. E-mail: wanglei1692@163.com
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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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