Operator-ordering identities for mutual transformation of power of coordinate-momentum operators obtained by a new concise method

Fan Hong-Yi; Lou Sen-Yue; Zhang Peng-Fei

doi:10.7498/aps.64.160302

Abstract

Since the foundation of quantum mechanics, operator-ordering identities for mutual transformation of power of coordinate-momentum operators have been a fundamental and tough topic. To the best of our knowledge, this topic has not been tackled smoothly because there is no elegant and direct way to investigate it. In this paper we report a very concise and novel method to handle this topic, i.e., we employ the generating function of two-variable Hermite polynomial and the characteristics of ordered operators to derive a series of operator-ordering identities for mutual transformation of power of coordinate-momentum operators: they surly possess potential applications. The essence of our method lies in the fact that coordinate-momentum operators can be permutable within ordered product of operators, just as the scenarios in P-Q ordering, Q-P ordering and Weyl ordering. We also derive the integration transformation formula about two-variable Hermite polynomial in phase space. The correspondence relation between operator ordering and quantization recipe is established. The beauty of theoretical physics is embodied extensively in the paper.

Keywords:

Authors and contacts

1.
Department of Physics, Ningbo University, Ningbo 315211, China;
2.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11175113).

References

[1]	Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[2]	Fan H Y, Zhan D H 2014 Chin. Phys. B 23 060301
[3]	Fan H Y, Lou S Y 2013 Sci. China: Phys. Mech. Astron. 56 2042
[4]	Fan H Y, Lou S Y, Pan X Y, Da C 2014 Acta Phys. Sin. 63 110304 (in Chinese) [范洪义, 楼森岳, 潘孝胤, 笪诚 2014 物理学报 63 110304]
[5]	Fan H Y 2014 Acta Phys. Sin. 63 020302 (in Chinese) [范洪义 2014 物理学报 63 020302]
[6]	Fan H Y 1992 J. Phys. A 25 3443
[7]	Fan H Y, Liang Z F 2015 Acta Phys. Sin. 64 050301 (in Chinese) [范洪义, 梁祖峰 2015 物理学报 64 050301]

Cited By

[1]	Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[2]	Fan H Y, Zhan D H 2014 Chin. Phys. B 23 060301
[3]	Fan H Y, Lou S Y 2013 Sci. China: Phys. Mech. Astron. 56 2042
[4]	Fan H Y, Lou S Y, Pan X Y, Da C 2014 Acta Phys. Sin. 63 110304 (in Chinese) [范洪义, 楼森岳, 潘孝胤, 笪诚 2014 物理学报 63 110304]
[5]	Fan H Y 2014 Acta Phys. Sin. 63 020302 (in Chinese) [范洪义 2014 物理学报 63 020302]
[6]	Fan H Y 1992 J. Phys. A 25 3443
[7]	Fan H Y, Liang Z F 2015 Acta Phys. Sin. 64 050301 (in Chinese) [范洪义, 梁祖峰 2015 物理学报 64 050301]

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Catalog

Vol. 64, Issue 16 - 2015-08-20

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