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The Invariant Eigen-operator (IEO) method is widely used in solving the eigenfrequencies of the coulped quantum mesoscopic circuits. The previous IEO method is complicated but stylized, we always wasted much time in this boring processes. Here we extended the IEO method to the matrix form based on Lagrangian of the complex mesoscopic circuits, and express the ideas and processes of the previous calculations of the IEO method in a very simple matrix form. The mathematical methods we used is the indicator representation of the matrix, and we got a very simple and convenient matrix form of the IEO method. This form has important significance for the calculation of large-scale complex multi-loop mesoscopic circuits. Moreover, the matrix form of the IEO method is very friendly to the programming implementation of the complex quantum mesoscopic L−C circuits, it is probably a most optimal algorithm for calculating the eigenfrequencies of the quantum mesoscopic L−C circuits. In addition, with some help of computer programs, we used this method to calculate the eigenfrequencies of three L−C mesoscopic circuits, including two cases with and without mutual inductance. We revealed some relevant properties of these circuits by calculating results, indicating that the eigenfrequency is only related to the element properties of the mesoscopic circuit itself. Finally, we found that this method can also be used in other areas like atom-light coupling systems and solid state physics.
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Keywords:
- invariant eigen-operator method /
- mesoscopic circuits /
- eigenfrequency
[1] Fan H Y, Li C 2004 Phys. Lett. A 321 75
Google Scholar
[2] 任益充, 范洪义 2013 物理学报 62 156301
Google Scholar
Ren Y C, Fan H Y 2013 Acta Phys. Sin. 62 156301
Google Scholar
[3] 范洪义, 吴昊, 袁洪春 2011 量子力学的不变本征算符方法 (上海: 上海交通大学出版社) 第175−178页
Fan H Y, Wu H, Yuan H C 2011 Invariant Eigen-Operator Method in Quantum Mechanics (Shanghai: Shanghai Jiao Tong University Press) pp175−178 (in Chinese)
[4] Fan H Y, Wu H, Xu X F 2005 Int. J. Mod. Phys. B 19 4073
Google Scholar
[5] Fan H Y, Tang X B 2007 Commun. Theor. Phys. 47 865
Google Scholar
[6] Ren G, Fan H Y 2009 Int. J. Phys. 48 2016
Google Scholar
[7] Fan H Y, Wang T T 2007 Int. J. Mod. Phys. B 21 1961
Google Scholar
[8] Song T Q, Fan H Y 2006 Mod. Phys. Lett. A 21 451
Google Scholar
[9] Liu Y M 2009 Int. J. Theor. Phys. 48 2372
Google Scholar
[10] Fan H Y, Tang X B 2006 Commun. Theor. Phys. 46 603
Google Scholar
[11] Fan H Y, Tang X B, Hu H P 2008 Commun. Theor. Phys. 50 674
Google Scholar
[12] Fan H Y, Wu H 2007 Mod. Phys. Lett. B 21 1751
Google Scholar
[13] Fan H Y, Wu H 2008 Commun. Theor. Phys. 49 50
Google Scholar
[14] Tang X B, Fan H Y 2010 Int. J. Theor. Phys. 49 877
Google Scholar
[15] Fan H Y, Wu H 2009 Int. J. Mod. Phys. B 23 234
[16] Fan H Y, Wang T T, Yang Y L 2006 Int. J. Mod. Phys. B 20 5417
Google Scholar
[17] Song T Q, Zhu J Y, Fan H Y 2003 Commun. Theor. Phys. 39 91
Google Scholar
[18] Fan H Y, Tang X B 2006 Commun. Theor. Phys. 45 1003
Google Scholar
[19] Fan H Y, Gui W J, Gui J Z 2007 Int. J. Mod. Phys. B 21 737
Google Scholar
[20] Yu T X, Fan H Y 2010 Commun. Theor. Phys. 53 257
Google Scholar
[21] Meng X G, Wang J S, Zhai Y, Fan H Y 2008 Chin. Phys. Lett. 25 1205
Google Scholar
[22] 张科, 范承玉, 范洪义 2018 物理学报 67 170301
Google Scholar
Zhang K, Fan C Y, Fan H Y, 2018 Acta Phys. Sin. 67 170301
Google Scholar
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[1] Fan H Y, Li C 2004 Phys. Lett. A 321 75
Google Scholar
[2] 任益充, 范洪义 2013 物理学报 62 156301
Google Scholar
Ren Y C, Fan H Y 2013 Acta Phys. Sin. 62 156301
Google Scholar
[3] 范洪义, 吴昊, 袁洪春 2011 量子力学的不变本征算符方法 (上海: 上海交通大学出版社) 第175−178页
Fan H Y, Wu H, Yuan H C 2011 Invariant Eigen-Operator Method in Quantum Mechanics (Shanghai: Shanghai Jiao Tong University Press) pp175−178 (in Chinese)
[4] Fan H Y, Wu H, Xu X F 2005 Int. J. Mod. Phys. B 19 4073
Google Scholar
[5] Fan H Y, Tang X B 2007 Commun. Theor. Phys. 47 865
Google Scholar
[6] Ren G, Fan H Y 2009 Int. J. Phys. 48 2016
Google Scholar
[7] Fan H Y, Wang T T 2007 Int. J. Mod. Phys. B 21 1961
Google Scholar
[8] Song T Q, Fan H Y 2006 Mod. Phys. Lett. A 21 451
Google Scholar
[9] Liu Y M 2009 Int. J. Theor. Phys. 48 2372
Google Scholar
[10] Fan H Y, Tang X B 2006 Commun. Theor. Phys. 46 603
Google Scholar
[11] Fan H Y, Tang X B, Hu H P 2008 Commun. Theor. Phys. 50 674
Google Scholar
[12] Fan H Y, Wu H 2007 Mod. Phys. Lett. B 21 1751
Google Scholar
[13] Fan H Y, Wu H 2008 Commun. Theor. Phys. 49 50
Google Scholar
[14] Tang X B, Fan H Y 2010 Int. J. Theor. Phys. 49 877
Google Scholar
[15] Fan H Y, Wu H 2009 Int. J. Mod. Phys. B 23 234
[16] Fan H Y, Wang T T, Yang Y L 2006 Int. J. Mod. Phys. B 20 5417
Google Scholar
[17] Song T Q, Zhu J Y, Fan H Y 2003 Commun. Theor. Phys. 39 91
Google Scholar
[18] Fan H Y, Tang X B 2006 Commun. Theor. Phys. 45 1003
Google Scholar
[19] Fan H Y, Gui W J, Gui J Z 2007 Int. J. Mod. Phys. B 21 737
Google Scholar
[20] Yu T X, Fan H Y 2010 Commun. Theor. Phys. 53 257
Google Scholar
[21] Meng X G, Wang J S, Zhai Y, Fan H Y 2008 Chin. Phys. Lett. 25 1205
Google Scholar
[22] 张科, 范承玉, 范洪义 2018 物理学报 67 170301
Google Scholar
Zhang K, Fan C Y, Fan H Y, 2018 Acta Phys. Sin. 67 170301
Google Scholar
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