Quantum mechanics mixed state representation

Fan Hong-Yi; Lou Sen-Yue; Pan Xiao-Yin; Da Cheng

doi:10.7498/aps.63.190302

Abstract

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

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).

References

[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)]

Cited By

[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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Catalog

Vol. 63, Issue 19 - 2014-10-05

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