广义n维耦合谐振子体系的代数解法

金明杰; 谭磊

doi:10.7498/aps.61.140301

摘要

利用二次型理论,通过三次保对易线性变换,实现了广义n维耦合谐振子体系哈密顿量的退耦合, 得到了体系对角化后的哈密顿量,并给出了体系的能量本征值和本征函数.

关键词:

Using the quadratic form theory, we achieve the decoupling of systematic Hamiltonian of generalization of n-dimensional coupled harmonic oscillators and derive the diagonalized Hamiltonian by three linear transformations with keeping the commutation relations unchanged. The energy eigenvalue and the eigenfunction of the system are also obtained.

Keywords:

generalization of n-dimensional coupled harmonic oscillators /
quadratic form theory /
diagonalization

作者及机构信息

金明杰¹,
谭磊^{1 2}

1.
兰州大学理论物理研究所, 兰州 730000;

2.
兰州大学磁学与磁性材料教育部重点实验室, 兰州 730000

基金项目: 国家自然科学基金(批准号: 10704031)、中央高校基金(批准号: lzujbky-2010-75)和兰州大学学生创新创业行动计划资助的课题.

Authors and contacts

Jin Ming-Jie¹,
Tan Lei^{1 2}

1.
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;

2.
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou 730000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10704031), the Fundamental Research Funds for the Central Universities, China ( Grant No. lzujbky-2010-75) and the Students' Innovative Entrepreneurial Action Plan of Lanzhou University, China.

参考文献

[1]	Walls D F, Milburn G J 1994 Quantum Optics (Berlin: Springer) p73
[2]	Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer) p168
[3]	Michelot F 1992 Phys. Rev. A 45 4271
[4]	Fan H Y 1993 Phys. Rev. A 47 2379
[5]	Joglekar Y N, Thompson C, Vemuri G 2011 Phys. Rev. A 83 063817
[6]	Wang S, Jiang J J, Xu S M, Li H Q 2010 Chin. Phys. B 19 014208
[7]	de Ponte M A, Mizrahi S S, Moussa M H Y 2007 Phys. Rev. A 76 032101
[8]	Kumar J, Sinha S, Sreeram P A 2009 Phys. Rev. E 80 031130
[9]	Dattagupta S, Kumar J, Sinha S, Sreeram P A 2010 Phys. Rev. E 81 031136
[10]	Xie B H, Jin S, Yan W X, Duan S Q, Zhao X G 2004 Eur. Phys. J. D 30 411
[11]	Cerveró J M, Lejarreta J D 1996 J. Phys. A: Math. Gen. 29 7545
[12]	Jin S, Xie B H, Zhang H B, Ge M L 2004 Commun. Theor. Phys. 42 681
[13]	Ling R L, Feng J, Feng J F 2010 Acta Phys. Sin. 59 8348 (in Chinese) [凌瑞良, 冯进, 冯金福 2010 物理学报 59 8348]
[14]	Xu S M, Jiang J J, Li H Q, Xu X L 2008 Acta Phys. Sin. 57 7430 (in Chinese) [徐世民, 蒋继建, 李洪奇, 徐兴磊 2008 物理学报 57 7430]
[15]	Ling R L, Feng J F 2009 Acta Phys. Sin. 58 2164 (in Chinese) [凌瑞良, 冯金福 2009 物理学报 58 2164]
[16]	Ling R L, Feng J F, Hu Y 2010 Acta Phys. Sin. 59 759 (in Chinese) [凌瑞良, 冯金福, 胡云 2010 物理学报 59 759]
[17]	Fan H Y, Yan P 2007 Commun. Theor. Phys. 48 428
[18]	Xu S M, Xu X L, Li H Q, Wang J S 2009 Chin. Phys. B 18 2129
[19]	Xu S M, Xu X L, Li H Q, Wang J S 2009 Acta Phys. Sin. 58 2174 (in Chinese) [徐世民, 徐兴磊, 李洪奇, 王继锁 2009 物理学报 58 2174]
[20]	Zhao C Y, Tan W H, Guo Q Z 2003 Acta Phys. Sin. 52 2694 (in Chinese) [赵超樱, 谭维翰, 郭奇志 2003 物理学报 52 2694]
[21]	Tan W H, Li Y F, Zhang W P 1988 Acta Phys. Sin. 37 396 (in Chinese) [谭维翰, 李宇舫, 张卫平 1988 物理学报 37 396]
[22]	Xu S M, Xu X L, Li H Q 2008 Int. J. Theor. Phys. 47 1654
[23]	Fan H Y 2005 From Quantum Mechanics to Quantum Optics (Shanghai: Shanghai Jiao Tong University Press) p344 (in Chinese) [范洪义 2005 从量子力学到量子光学(上海:上海交通大学出版社) 第344页]

施引文献

[1]	Walls D F, Milburn G J 1994 Quantum Optics (Berlin: Springer) p73
[2]	Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer) p168
[3]	Michelot F 1992 Phys. Rev. A 45 4271
[4]	Fan H Y 1993 Phys. Rev. A 47 2379
[5]	Joglekar Y N, Thompson C, Vemuri G 2011 Phys. Rev. A 83 063817
[6]	Wang S, Jiang J J, Xu S M, Li H Q 2010 Chin. Phys. B 19 014208
[7]	de Ponte M A, Mizrahi S S, Moussa M H Y 2007 Phys. Rev. A 76 032101
[8]	Kumar J, Sinha S, Sreeram P A 2009 Phys. Rev. E 80 031130
[9]	Dattagupta S, Kumar J, Sinha S, Sreeram P A 2010 Phys. Rev. E 81 031136
[10]	Xie B H, Jin S, Yan W X, Duan S Q, Zhao X G 2004 Eur. Phys. J. D 30 411
[11]	Cerveró J M, Lejarreta J D 1996 J. Phys. A: Math. Gen. 29 7545
[12]	Jin S, Xie B H, Zhang H B, Ge M L 2004 Commun. Theor. Phys. 42 681
[13]	Ling R L, Feng J, Feng J F 2010 Acta Phys. Sin. 59 8348 (in Chinese) [凌瑞良, 冯进, 冯金福 2010 物理学报 59 8348]
[14]	Xu S M, Jiang J J, Li H Q, Xu X L 2008 Acta Phys. Sin. 57 7430 (in Chinese) [徐世民, 蒋继建, 李洪奇, 徐兴磊 2008 物理学报 57 7430]
[15]	Ling R L, Feng J F 2009 Acta Phys. Sin. 58 2164 (in Chinese) [凌瑞良, 冯金福 2009 物理学报 58 2164]
[16]	Ling R L, Feng J F, Hu Y 2010 Acta Phys. Sin. 59 759 (in Chinese) [凌瑞良, 冯金福, 胡云 2010 物理学报 59 759]
[17]	Fan H Y, Yan P 2007 Commun. Theor. Phys. 48 428
[18]	Xu S M, Xu X L, Li H Q, Wang J S 2009 Chin. Phys. B 18 2129
[19]	Xu S M, Xu X L, Li H Q, Wang J S 2009 Acta Phys. Sin. 58 2174 (in Chinese) [徐世民, 徐兴磊, 李洪奇, 王继锁 2009 物理学报 58 2174]
[20]	Zhao C Y, Tan W H, Guo Q Z 2003 Acta Phys. Sin. 52 2694 (in Chinese) [赵超樱, 谭维翰, 郭奇志 2003 物理学报 52 2694]
[21]	Tan W H, Li Y F, Zhang W P 1988 Acta Phys. Sin. 37 396 (in Chinese) [谭维翰, 李宇舫, 张卫平 1988 物理学报 37 396]
[22]	Xu S M, Xu X L, Li H Q 2008 Int. J. Theor. Phys. 47 1654
[23]	Fan H Y 2005 From Quantum Mechanics to Quantum Optics (Shanghai: Shanghai Jiao Tong University Press) p344 (in Chinese) [范洪义 2005 从量子力学到量子光学(上海:上海交通大学出版社) 第344页]

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广义n维耦合谐振子体系的代数解法

An algebraic approach to the generalization of n-dimensional coupled harmonic oscillators system

摘要

Abstract

作者及机构信息

1.
兰州大学理论物理研究所, 兰州 730000;

2.
兰州大学磁学与磁性材料教育部重点实验室, 兰州 730000

Authors and contacts

1.
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;

2.
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou 730000, China

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广义n维耦合谐振子体系的代数解法

An algebraic approach to the generalization of n-dimensional coupled harmonic oscillators system

摘要

Abstract

作者及机构信息

1. 兰州大学理论物理研究所, 兰州 730000; 2. 兰州大学磁学与磁性材料教育部重点实验室, 兰州 730000

Authors and contacts

1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; 2. Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou 730000, China

参考文献

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目录

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作者中心

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关于期刊

关于我们

1.
兰州大学理论物理研究所, 兰州 730000;

2.
兰州大学磁学与磁性材料教育部重点实验室, 兰州 730000

1.
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;

2.
Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou 730000, China