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In non-commutative spaces the invariant eigen-operator method is used to derive and calculate Hamiltonian spectra for three kinds of three coupled harmonic oscillators: no coupling, coordinate coupling and momentum coupling. According to the comparison with the results in commutative space, it is shown that when the non-commutative parameter is zero the obtained energy levels are equal to the energy levels in commutative space. Finally the effect of the coupling coefficient on Hamiltonian spectrum in non-commutative space is discussed.
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Keywords:
- invariant eigen-operator method /
- non-commutation spaces /
- Hamiltonian spectrum for three coupled harmonic oscillators /
- the energy levels
[1] Deng F G, Li X H, Li C Y, Zhou P, Zhou H Y 2007 Chin. Phys. 16 0277
[2] Wang Z Y, Xiong C D 2008 Chin. Phys. B 17 4170
[3] Wang Z Y, Xiong C D,He B 2008 Chin. Phys. B 17 3985
[4] Lu Z X 2007 Chin. Phys. 16 0635
[5] Lu G Y, Pan F 2007 Acta Phys. Sin. 56 1895 (in Chinese)[鲁国英、 潘 峰 2007 56 1895]
[6] Wang Z Y, Xiong C D 2007 Acta Phys. Sin. 56 3070 (in Chinese)[王智勇、 熊彩东 2007 56 3070]
[7] Tian J, Qiu H B, Chen Y 2010 Acta Phys. Sin. 59 3763 (in Chinese) [田 静、 邱海波、 陈 勇 2010 59 3736]
[8] Chen Z J, Ning X J 2003 Acta Phys.Sin. 52 2683 (in Chinese) [陈增军、 宁西京 2003 52 2683]
[9] Huang B W, Wang D Y 2002 Acta Phys. Sin. 51 1163 (in Chinese) [黄博文、 王德云 2002 51 1163]
[10] Muthukumar B, Mitra P 2002 Phys. Rev. D 66 027701
[11] Szabo R J 2003 Phys. Rep. 378 207
[12] Douglas M R, Nekrasov M A 2001 Rev. Mod. Phys. 73 977
[13] WU H 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) p60—69 (in Chinese) [吴 昊 2008 博士学位论文 (合肥: 中国科学技术大学)第60—69页]
[14] Lerbfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[15] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[16] Jing S C, Liu Q Y, Fan H Y 2005 J. Phys. A 38 8409
[17] Fan H Y, Tang X B, Wang T T 2007 Commu. Theor. Phys. 48 633
[18] Jing S C, Fan H Y 2005 Modern Physics Letters A 20 691
[19] Fang H Y 2008 Advance in Mathematical Basis of Quantum Mechanics (Hefei: University of Science and Technology of China Press) p313—351 (in Chinese) [范洪义 2008 量子力学数理基础进展(合肥:中国科学技术大学出版社)第313—351]
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[1] Deng F G, Li X H, Li C Y, Zhou P, Zhou H Y 2007 Chin. Phys. 16 0277
[2] Wang Z Y, Xiong C D 2008 Chin. Phys. B 17 4170
[3] Wang Z Y, Xiong C D,He B 2008 Chin. Phys. B 17 3985
[4] Lu Z X 2007 Chin. Phys. 16 0635
[5] Lu G Y, Pan F 2007 Acta Phys. Sin. 56 1895 (in Chinese)[鲁国英、 潘 峰 2007 56 1895]
[6] Wang Z Y, Xiong C D 2007 Acta Phys. Sin. 56 3070 (in Chinese)[王智勇、 熊彩东 2007 56 3070]
[7] Tian J, Qiu H B, Chen Y 2010 Acta Phys. Sin. 59 3763 (in Chinese) [田 静、 邱海波、 陈 勇 2010 59 3736]
[8] Chen Z J, Ning X J 2003 Acta Phys.Sin. 52 2683 (in Chinese) [陈增军、 宁西京 2003 52 2683]
[9] Huang B W, Wang D Y 2002 Acta Phys. Sin. 51 1163 (in Chinese) [黄博文、 王德云 2002 51 1163]
[10] Muthukumar B, Mitra P 2002 Phys. Rev. D 66 027701
[11] Szabo R J 2003 Phys. Rep. 378 207
[12] Douglas M R, Nekrasov M A 2001 Rev. Mod. Phys. 73 977
[13] WU H 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) p60—69 (in Chinese) [吴 昊 2008 博士学位论文 (合肥: 中国科学技术大学)第60—69页]
[14] Lerbfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[15] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 704
[16] Jing S C, Liu Q Y, Fan H Y 2005 J. Phys. A 38 8409
[17] Fan H Y, Tang X B, Wang T T 2007 Commu. Theor. Phys. 48 633
[18] Jing S C, Fan H Y 2005 Modern Physics Letters A 20 691
[19] Fang H Y 2008 Advance in Mathematical Basis of Quantum Mechanics (Hefei: University of Science and Technology of China Press) p313—351 (in Chinese) [范洪义 2008 量子力学数理基础进展(合肥:中国科学技术大学出版社)第313—351]
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