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

doi:10.1088/1674-1056/ab99aa

中国物理B ›› 2020, Vol. 29 ›› Issue (10): 100301-.doi: 10.1088/1674-1056/ab99aa

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^,‡(), Ji-Suo Wang(王继锁)²

收稿日期:2020-03-15 修回日期:2020-05-12 接受日期:2020-06-05 出版日期:2020-10-05 发布日期:2020-10-05
通讯作者: Xing-Lei Xu(徐兴磊), Lei Wang(王磊)

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

Received:2020-03-15 Revised:2020-05-12 Accepted:2020-06-05 Online:2020-10-05 Published:2020-10-05
Contact: ^†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).

摘要/Abstract

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.

Key words: Fock space, new polynomial, ordered product, analogy method

中图分类号: (Quantum mechanics)

03.65.-w

03.67.-a (Quantum information) 89.70.-a (Information and communication theory)

Shi-Min Xu(徐世民), Yu-Shan Li(李玉山), Xing-Lei Xu(徐兴磊), Lei Wang(王磊), Ji-Suo Wang(王继锁). [J]. 中国物理B, 2020, 29(10): 100301-.

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[J]. Chin. Phys. B, 2020, 29(10): 100301-.

参考文献 16

[1]	Glauber R J 1963 Phys. Rev. 131 2766 DOI: 10.1103/PhysRev.131.2766
[2]	Dirac P A M 1985 Principles of Quantum Mechanics Oxford Oxford University Press
[3]	Scully M O, Zubairy M S 1997 Quantum Optics Cambridge Cambridge University Press
[4]	Xu S M, Zhang Y H, Xu X L, Li H Q, Wang J S 2016 Chin. Phys. B 25 120301 DOI: 10.1088/1674-1056/25/12/120301
[5]	Fan H Y 2012 Sci. China-Phys. Mech. Astron. 55 762 DOI: 10.1007/s11433-012-4699-4
[6]	Lee H W 1995 Phys. Rep. 259 147 DOI: 10.1016/0370-1573(95)00007-4
[7]	Balazs N L, Jenning B K 1984 Phys. Rep. 104 347 DOI: 10.1016/0370-1573(84)90151-0
[8]	Wang J S, Fan H Y, Meng X G 2012 Chin. Phys. B 21 064204 DOI: 10.1088/1674-1056/21/6/064204
[9]	Meng X G, Wang J S, Liang B L 2009 Chin. Phys. B 18 1534 DOI: 10.1088/1674-1056/18/4/040
[10]	Xu S M, Zhang Y H, Xu X L 2012 Coll. Phys. 31 1
[11]	Xu S M, Zhang Y H, Xu X L, Li H Q, Wang J S 2020 Int. J. Theor. Phys. 59 539 DOI: 10.1007/s10773-019-04347-6
[12]	Mansour T, Matthias S 2016 Commutation Relations, Normal Ordering, and Stirling Numbers Boca Raton CRC Press 63 65
[13]	Lambert F, Springael J 2008 Acta Appl. Math. 102 147 DOI: 10.1007/s10440-008-9209-3
[14]	Shen Y J, Gao Y T, Yu X, Meng G Q, Qin Y 2014 Appl. Math. Comp. 227 502 DOI: 10.1016/j.amc.2013.11.005
[15]	Erdelyi A 1953 Higher Transcendental Function: The Batemann Manuscript Project New York McGraw-Hill
[16]	Hu L Y, Fan H Y 2009 Chin. Phys. B 18 1061 DOI: 10.1088/1674-1056/18/3/037

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

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