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Chin. Phys. B, 2020, Vol. 29(5): 050303    DOI: 10.1088/1674-1056/ab7dbd
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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
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.
Keywords:  normal and anti-normal orderings      parameter differential method of operators      intermediate coordinate-momentum representation  
Received:  18 February 2020      Published:  05 May 2020
PACS:  03.65.-w (Quantum mechanics)  
  42.50.-p (Quantum optics)  
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

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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