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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.
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Keywords:
- generalization of n-dimensional coupled harmonic oscillators /
- quadratic form theory /
- diagonalization
[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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[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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