相空间中对应量子力学基本对易关系的积分变换及求Wigner函数的新途径

范洪义; 梁祖峰

doi:10.7498/aps.64.050301

摘要

本文指出相空间中存在有对应量子力学基本对易关系积分变换, 其积分核是1/exp[2i(q-Q) (p-P), 其中表示Weyl 排序, Q, P是坐标算符和动量算符, 其功能是负责算符的三种常用排序(P-Q排序、Q-P排序和Weyl 排序)规则之间的相互转化. 此外, 还导出了此积分核与Wigner 算符之间的关系, 以及Wigner函数在这类积分变换下的性质及用途.

关键词:

In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1/exp[2i(q-Q)(p-P)], here denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P-Q ordering, Q-P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained.

Keywords:

作者及机构信息

范洪义¹,
梁祖峰²

1.
宁波大学, 物理系, 宁波 315211;

2.
杭州师范大学, 理学院, 杭州 310036

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

Fan Hong-Yi¹,
Liang Zu-Feng²

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

2.
College of Science, Hangzhou Normal University, Hangzhou 310036, China

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

参考文献

[1]	Dragoman D 2002 Progress In Optics 42 424
[2]	Dragoman D, Dragoman M 1999 Prog. Quantum Electron. 23 131
[3]	Crasser O, Mack H, Schleich W P 2004 Fluct. Noise Lett. 04 L43
[4]	Nienhuis G, Allen L 1993 Phys. Rev. A 48 656
[5]	Wolf K B and Kurmyshev E V 1993 Phys. Rev. A 47 3365
[6]	Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[7]	L C H, Fan H Y, Jiang N Q 2010 Chin. Phys. B 19 120303
[8]	Fan H Y 2003 Phys. Lett. A 313 343
[9]	Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 014204
[10]	Weyl H 1927 Z. Phys. 46 1
[11]	Wigner E 1932 Phys. Rev. 40 749
[12]	Wang J S, Fan H Y, Meng X G 2012 Chin. Phys. B 21 064204
[13]	Fan H Y 1992 J. Phys. A 25 3443
[14]	Fan H Y 1997 Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics—Progress of Dirac's Symbolic Method (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [范洪义1997 量子力学表象与变换论-狄拉克符号法进展(上海: 上海科技出版社)
[15]	Fan H Y 2008 Commun. Theor. Phys. 50 935
[16]	Fan H Y 2013 Acta Phys. Sin. 62 020302 (in Chinese) [范洪义 2013 物理学报 62 020302]

施引文献

[1]	Dragoman D 2002 Progress In Optics 42 424
[2]	Dragoman D, Dragoman M 1999 Prog. Quantum Electron. 23 131
[3]	Crasser O, Mack H, Schleich W P 2004 Fluct. Noise Lett. 04 L43
[4]	Nienhuis G, Allen L 1993 Phys. Rev. A 48 656
[5]	Wolf K B and Kurmyshev E V 1993 Phys. Rev. A 47 3365
[6]	Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[7]	L C H, Fan H Y, Jiang N Q 2010 Chin. Phys. B 19 120303
[8]	Fan H Y 2003 Phys. Lett. A 313 343
[9]	Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 014204
[10]	Weyl H 1927 Z. Phys. 46 1
[11]	Wigner E 1932 Phys. Rev. 40 749
[12]	Wang J S, Fan H Y, Meng X G 2012 Chin. Phys. B 21 064204
[13]	Fan H Y 1992 J. Phys. A 25 3443
[14]	Fan H Y 1997 Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics—Progress of Dirac's Symbolic Method (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [范洪义1997 量子力学表象与变换论-狄拉克符号法进展(上海: 上海科技出版社)
[15]	Fan H Y 2008 Commun. Theor. Phys. 50 935
[16]	Fan H Y 2013 Acta Phys. Sin. 62 020302 (in Chinese) [范洪义 2013 物理学报 62 020302]

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