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Recast combination functions of coordinate and momentum operators into their ordered product forms |
| Lei Wang(王磊)1,2, Xiang-Guo Meng(孟祥国)3, Ji-Suo Wang(王继锁)1 |
1 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
2 College of Physics and Electronic Engineering, Heze University, Heze 274015, China;
3 Shandong Provincial Key Laboratory of Optical Communication Science and Technology, School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China |
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Abstract By using the parameter differential method of operators, we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings, which is more ecumenical, simpler, and neater than the existing ways. These products are very useful in obtaining some new differential relations and useful mathematical integral formulas. Further, we derive the normally ordered form of the operator (fQ+gP)-n with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate-momentum representation. In addition, general mutual transformation rules of the normal and anti-normal orderings, which have good universality, are derived and hence the anti-normal ordering of (fQ+gP)-n is also obtained. Finally, the application of some new identities is given.
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Received: 18 February 2020
Accepted manuscript online:
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PACS:
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03.65.-w
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(Quantum mechanics)
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42.50.-p
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(Quantum optics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11347026), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011), and the Natural Science Foundation of Heze University, China (Grant Nos. XY17KJ09 and XY18PY13). |
Corresponding Authors:
Ji-Suo Wang
E-mail: jswang@qfnu.edu.cn
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Cite this article:
Lei Wang(王磊), Xiang-Guo Meng(孟祥国), Ji-Suo Wang(王继锁) Recast combination functions of coordinate and momentum operators into their ordered product forms 2020 Chin. Phys. B 29 050303
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| [1] |
Mansour T and Schork M 2008 Russ. J. Math. Phys. 15 77
|
| [2] |
Witschel W 2005 Phys. Lett. A 334 140
|
| [3] |
Schleich W P 2001 Quantum Optics in Phase Space (New York: Wiley)
|
| [4] |
Meng X G, Goan H S, Wang J S and Zhang R 2018 Opt. Commun. 411 15
|
| [5] |
Wang Z, Meng X G and Fan H Y 2012 J. Opt. Soc. Am. B 29 397
|
| [6] |
Ballentine L E 1998 Quantum mechanics: Modern Development (Singapore: World Scientific)
|
| [7] |
Meng X G, Wang J S and Fan H Y 2011 Opt. Commun. 284 2070
|
| [8] |
Wang J S, Meng X G and Fan H Y 2015 Chin. Phys. B 24 014203
|
| [9] |
Dirac P A M 1985 Principles of Quantum Mechanics (Oxford: Oxford University Press)
|
| [10] |
Du C X, Meng X G, Zhang R and Wang J S 2017 Chin. Phys. B 26 120301
|
| [11] |
Klauder J R and Skagerstam B S 1985 Coherence States (Singapore: World Scientific)
|
| [12] |
Glauber R J 1963 Phys. Rev. 130 2529
|
| [13] |
Fan H Y and Fan Y 2002 Commun. Theor. Phys. 38 297
|
| [14] |
Fan H Y 1991 Phys. Lett. A 161 1
|
| [15] |
Louisell W H 1973 Quantum Statistical Properties of Radiation (New York: Wiley)
|
| [16] |
Perelomov A M 1986 Generalized Coherent States and their Applications (Berlin: Springer)
|
| [17] |
Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321 480
|
| [18] |
Yuan, H C, Xu, X X, Lei H M, Xu Y J and Meng X G 2020 Can. J. Phys. 98 119
|
| [19] |
Wang J S, Fan H Y and Meng X G 2012 Chin. Phys. B 21 064204
|
| [20] |
Wünsche A 1999 J. Opt. B-Quantum Semicl. Opt. 1 R11
|
| [21] |
Fan H Y 2008 Ann. Phys. 323 1502
|
| [22] |
Meng X G, Wang J S and Liang B L 2009 Chin. Phys. B 18 1534
|
| [23] |
Shao Y C and Fan H Y 2008 Commun. Theor. Phys. 49 866
|
| [24] |
Li H M and Yuan H C 2010 Int. J. Theor. Phys. 49 2121
|
| [25] |
Fan H Y 1992 J. Phys. A: Math. Gen. 25 1013
|
| [26] |
Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
|
| [27] |
Lv H Y, Wang J S, Zhang X Y, Wu M Y, Liang B L and Meng X G 2019 Chin. Phys. B 28 090302
|
| [28] |
Meng X G, Liu J M, Wang J S and Fan H Y 2019 Eur. Phys. J. D. 73 32
|
| [29] |
Xu S M, Zhang Y H, Xu X L, Li H Q and Wang J S 2016 Chin. Phys. B 25 120301
|
| [30] |
Fan H Y 2001 Entangled State Representations in Quantum Mechanics and Their Applications (Shanghai: Shanghai Jiao Tong University Press) (in Chinese)
|
| [31] |
Wang J S, Meng X G and Fan H Y 2017 J. Mod. Opt. 64 1398
|
| [32] |
Meng X G, Wang Z, Fan H Y and Wang J S 2012 J. Opt. Soc. Am. B 29 3141
|
| [33] |
Wang Z X and Guo D R 1965 General Theory of Special Functions (Beijing: Science Press) (in Chinese)
|
| [34] |
Fan H Y and Fu L 2003 J. Phys. A: Math. Gen. 36 4987
|
| [35] |
Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific and Technical Press) (in Chinese)
|
| [36] |
Meng X G, Wang J S, Yang Z S, Zhang X Y, Zhang Z T, Liang B L and Li K C 2020 J. Opt. 22 015201
|
| [37] |
Meng X G, Wang Z, Wang J S and Fan H Y 2013 J. Opt. Soc. Am. B 30 1614
|
| [38] |
Rainville E D 1960 Special functions (New York: MacMillan Comp.)
|
| [39] |
Wang Z, Meng X G, Li H M and Yuan H C 2014 Int. J. Mod. Phys. B 28 1450115
|
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