量子力学混合态表象

范洪义; 楼森岳; 潘孝胤; 笪诚

doi:10.7498/aps.63.190302

摘要

在以往的文献中量子力学的表象都是纯态表象，在本文中我们从算符的合理排序和概率统计的正态分布思想出发，首次提出了量子力学混合态表象的概念，并证明了其完备性和正交性.量子力学混合态表象的优点是可以反映算符的多种表示以及其相应的排序规则.

关键词:

In the previous studies and literatures, quantum mechanics representations are a pure state representation, while in this paper beginning with reasonable ordering of operators in quantum mechanics and the normal distribution thought in probability statistics, we propose the concept of quantum mechanics mixed state representation firstly,and prove its completeness and orthogonality. The advantages of mixed state representation is that it can reflect a variety of expression of quantum mechanics operators and the corresponding operators ordering rules.

Keywords:

quantum mechanics mixed state representation /
quantum mechanics pure state representation /
ordering rules /
IWOP technique

作者及机构信息

1.
宁波大学物理系, 宁波 315211;

2.
中国科学技术大学材料科学与工程系, 合肥 230026

基金项目: 国家自然科学基金（批准号：11175113，11275123）资助的课题.

Authors and contacts

1.
Department of Physics, Ningbo University, Ningbo 315211, China;

2.
Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113, 11275123).

参考文献

[1]	Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford: Clarendon Press)
[2]	Klauder J R and Skagerstam B S 1985 coherent States: Application in Physics and Mathematical Physics (Singapore: World Scientific)
[3]	Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[4]	Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[5]	Fan H Y 2012 Representation and Transformation Theory in Quantum Mechanics-Progress of Dirac's Symbolic Method (2nd Ed.) (Hefei: USTC Press) (in Chinese) [范洪义 2012 量子力学表象与变换论–狄拉克符号法进展 (第2版) (合肥: 中国科学技术大学出版社)]
[6]	Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[7]	Fan H Y, Tang X B 2008 Devolopment of basis of the mathematical physics of quantum mechanics (Hefei: USTC Press) (in Chinese) [范洪义, 唐绪兵 2008 量子力学数理基础进展 (合肥: 中国科学技术大学出版社)]
[8]	Fan H Y, Yuan H C 2012 From squeezed state to coherent state (Hefei: USTC Press) (in Chinese) [范洪义, 袁洪春 2012 从压缩态到相干态 (合肥: 中国科学技术大学出版社)]
[9]	Fan H Y, Da C 2013 Chin. Phys. B 22 090303
[10]	Zhou G R 1984 Probability and Statistics (Beijing: Higher Education Press) (in Chinese) [周概容 1984 概率论与数理统计 (北京: 高等教育出版社)]

施引文献

[1]	Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford: Clarendon Press)
[2]	Klauder J R and Skagerstam B S 1985 coherent States: Application in Physics and Mathematical Physics (Singapore: World Scientific)
[3]	Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[4]	Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[5]	Fan H Y 2012 Representation and Transformation Theory in Quantum Mechanics-Progress of Dirac's Symbolic Method (2nd Ed.) (Hefei: USTC Press) (in Chinese) [范洪义 2012 量子力学表象与变换论–狄拉克符号法进展 (第2版) (合肥: 中国科学技术大学出版社)]
[6]	Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[7]	Fan H Y, Tang X B 2008 Devolopment of basis of the mathematical physics of quantum mechanics (Hefei: USTC Press) (in Chinese) [范洪义, 唐绪兵 2008 量子力学数理基础进展 (合肥: 中国科学技术大学出版社)]
[8]	Fan H Y, Yuan H C 2012 From squeezed state to coherent state (Hefei: USTC Press) (in Chinese) [范洪义, 袁洪春 2012 从压缩态到相干态 (合肥: 中国科学技术大学出版社)]
[9]	Fan H Y, Da C 2013 Chin. Phys. B 22 090303
[10]	Zhou G R 1984 Probability and Statistics (Beijing: Higher Education Press) (in Chinese) [周概容 1984 概率论与数理统计 (北京: 高等教育出版社)]

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