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量子力学坐标-动量算符幂次排序的相互转换是一个基本的量子力学课题, 本文提出了一个十分简捷有效的方法处理此问题, 即利用双变量厄米特多项式的母函数性质及有序算符记号内的算符特点, 给出一系列关于坐标-动量算符幂次排序的恒等式, 它们具有广泛的应用.
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关键词:
- 基本对易关系 /
- 双变量厄米特多项式的母函数
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:
- fundamental commutative relation /
- generating function of two-variable Hermite polynomials
[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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[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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