Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

doi:10.1088/1674-1056/19/9/090312

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90312-090312.doi: 10.1088/1674-1056/19/9/090312

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

范洪义, 陈俊华, 袁洪春

Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

收稿日期:2010-01-02 修回日期:2010-03-07 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10874174) and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070358009).

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

Fan Hong-Yi(范洪义), Chen Jun-Hua(陈俊华), and Yuan Hong-Chun (袁洪春)^†

Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Received:2010-01-02 Revised:2010-03-07 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10874174) and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070358009).

摘要/Abstract

摘要： For classical Hamiltonian with general form we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Abstract: For classical Hamiltonian with general form we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Key words: invariant eigen-operator method method, normal coordinates

中图分类号:

0365

范洪义, 陈俊华, 袁洪春. Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian[J]. 中国物理B, 2010, 19(9): 90312-090312.

Fan Hong-Yi(范洪义), Chen Jun-Hua(陈俊华), and Yuan Hong-Chun (袁洪春). Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian[J]. Chin. Phys. B, 2010, 19(9): 90312-090312.

[1]	Goldstein H, Poole J C P and Safko J L 2002 Classical Mechanics (Columbia University: Addison-Wesley)
[2]	Fan H Y and Chao L 2004 Phys. Lett. A 321 75
[3]	Fan H Y, Hu H P and Tang X B 2005 J. Phys. A: Math. Gen. 38 4391
[4]	Schrodinger E 1928 Four Lectures on Wave Mechanics (London: Blackie & Son)
[5]	Fan H Y 2005 From Quantum Mechanics to Quan-tum Optics\|Development of the Mathematical Physics (Shanghai: Shanghai Jiao Tong University Press) p349 (in Chinese)
[6]	Fan H Y and Tang X B 2008 Progress of Mathematical Physics in Quantum Mechanics in China (Shanghai: University of Science and Technology of China Press) p333 (in Chinese)

[1]	范洪义, 姜年权. Energy average formula of photon gas rederived by using the generalised Hermann–Feynman theorem[J]. 中国物理B, 2010, 19(9): 90301-090301.
[2]	强继业, 马松华, 方建平. Fusion and fission solitons for the (2+1)-dimensional generalized Breor–Kaup system[J]. 中国物理B, 2010, 19(9): 90305-090305.
[3]	刘堂昆, 单传家, 刘继兵, 范洪义. Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation[J]. 中国物理B, 2010, 19(9): 90307-090307.
[4]	卫高峰, 陈文利. Continuum states of modified Morse potential[J]. 中国物理B, 2010, 19(9): 90308-090308.
[5]	任学藻, 姜道来, 丛红璐, 黎雷. Exact solution of entanglement of the double Jaynes–Cummings model without rotating wave approximation[J]. 中国物理B, 2010, 19(9): 90309-090309.
[6]	何勇, 姜年权. Nondestructive and complete Bell-state analysis for atomic qubit systems[J]. 中国物理B, 2010, 19(9): 90310-090310.
[7]	程留永, 邵晓强, 张寿, Yeon Kyu-Hwang. Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model[J]. 中国物理B, 2010, 19(9): 90311-090311.
[8]	高丹, 赵振双, 朱爱东, 王洪福, 邵晓强, 张寿. Teleportation and thermal entanglement in two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski–Moriya interaction and the inhomogeneous magnetic field[J]. 中国物理B, 2010, 19(9): 90313-090313.
[9]	F. Tacskin, G. Koccak. Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term[J]. 中国物理B, 2010, 19(9): 90314-090314.
[10]	李明, 费少明, 李先清. Concurrence, tangle and fully entangled fraction[J]. 中国物理B, 2010, 19(9): 90315-090315.
[11]	袁文, 殷澄, 王贤平, 曹庄琪. Quantum reflection as the reflection of subwaves[J]. 中国物理B, 2010, 19(9): 93402-093402.
[12]	刘伟慈, 王发强, 梁瑞生. Concurrence evolution of two qubits coupled with one-mode cavity separately[J]. 中国物理B, 2010, 19(9): 94204-094204.
[13]	杨贞标, 吴怀志, 郑仕标. Robust generation of qutrit entanglement via adiabatic passage of dark states[J]. 中国物理B, 2010, 19(9): 94205-094205.
[14]	梁麦林, 袁兵. Entanglement transfer via the Raman atom–cavity-field interaction[J]. 中国物理B, 2010, 19(9): 94206-094206.
[15]	赵丽芳, 赖柏辉, 梅锋, 於亚飞, 冯勋立, 张智明. Generation of a four-particle entangled state via cross-Kerr nonlinearity[J]. 中国物理B, 2010, 19(9): 94207-094207.

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 6

相关文章 15

Metrics

本文评价

推荐阅读 0