光场位相算符和逆算符的Weyl编序展开

李学超; 杨阳; 范洪义

doi:10.7498/aps.62.080301

摘要

用有序算符内的积分技术, 推导了光场位相算符和逆算符的Weyl编序展开形式, 并利用该结果获得了相算符的经典对应以及某些新的特殊函数的生成函数和新的积分公式, 尤其是导出了带负次幂的复高斯积分的积分公式.

关键词:

Using the technique of integration within an ordered product of operators, we derive Weyl ordered expansion for optical field phase operator and inverse of creation and annhilation operators. The results are used to obtain the classical correspondence, new generation function formula of some special functions and new integration formulas. In particular, for the first time we derive complex Gaussian integral formula when the integrand has negative power function.

Keywords:

Weyl ordering /
phase operator /
integration within an ordered product of operators

作者及机构信息

1.
安徽理工大学理学院, 淮南 232001;

2.
中国科学技术大学近代物理系, 合肥 230026;

3.
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:10975125, 11175113)资助的课题.

Authors and contacts

1.
School of Science, Anhui University of Science and Technology, Huainan 232001, China;

2.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;

3.
Department of Material 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. 10975125, 11175113).

参考文献

[1]	Dirac P A M 1927 Proc. R. Soc. London A 114 243
[2]	Carruthers P, Nieto M M 1968 Rev. Mod. Phys. 40 411
[3]	Wigner E P 1932 Phys. Rev. 40 749
[4]	Klauder J R, Skagerstam B S 1985 Coherent States (Singerpore:World Scientific Publishing)
[5]	Scully M O, Zubairy M S 1997 Quantum Optics (United Kingdom:Cambridge University Press)
[6]	Glauber R J 1963 Phys. Rev. 130 2529
[7]	Weyl H 1927 Z. Phys. A 46 1
[8]	Fan H Y 1992 J. Phys. A 25 3443
[9]	Fan H Y, Hu L Y 2008 Chin. Phys. B 17 1640
[10]	Yuan H C, Xu X X 2010 Acta Phys. Sin. 61 064205 (in Chinese) [袁洪春, 徐学翔 2012 物理学报 61 064205]
[11]	Fan H Y 2008 Ann. Phys. 323 1502
[12]	Jiang N Q, Fan H Y, Hu L Y 2011 J. Phys. A:Math. Theor. 44 195302
[13]	Xu X X,Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]
[14]	Dirac P A M 1966 Lectures on Quantum Field Theory (New York:Academic)
[15]	Fan H Y 1993 Phys. Rev. A 47 4521

施引文献

[1]	Dirac P A M 1927 Proc. R. Soc. London A 114 243
[2]	Carruthers P, Nieto M M 1968 Rev. Mod. Phys. 40 411
[3]	Wigner E P 1932 Phys. Rev. 40 749
[4]	Klauder J R, Skagerstam B S 1985 Coherent States (Singerpore:World Scientific Publishing)
[5]	Scully M O, Zubairy M S 1997 Quantum Optics (United Kingdom:Cambridge University Press)
[6]	Glauber R J 1963 Phys. Rev. 130 2529
[7]	Weyl H 1927 Z. Phys. A 46 1
[8]	Fan H Y 1992 J. Phys. A 25 3443
[9]	Fan H Y, Hu L Y 2008 Chin. Phys. B 17 1640
[10]	Yuan H C, Xu X X 2010 Acta Phys. Sin. 61 064205 (in Chinese) [袁洪春, 徐学翔 2012 物理学报 61 064205]
[11]	Fan H Y 2008 Ann. Phys. 323 1502
[12]	Jiang N Q, Fan H Y, Hu L Y 2011 J. Phys. A:Math. Theor. 44 195302
[13]	Xu X X,Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]
[14]	Dirac P A M 1966 Lectures on Quantum Field Theory (New York:Academic)
[15]	Fan H Y 1993 Phys. Rev. A 47 4521

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