中国物理B ›› 2010, Vol. 19 ›› Issue (7): 70303-070303.doi: 10.1088/1674-1056/19/7/070303

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Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator

孟祥国1, 范洪义1, 王继锁2   

  1. (1)Department of Physics, Liaocheng University, Liaocheng 252059, China; (2)Department of Physics, Liaocheng University, Liaocheng 252059, China;Department of Physics, Qufu Normal University, Qufu 273165, China
  • 修回日期:2010-01-18 出版日期:2010-07-15 发布日期:2010-07-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10574060), the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23) and the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07).

Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator

Meng Xiang-Guo(孟祥国)a)†, Fan Hong-Yi(范洪义) a), and Wang Ji-Suo(王继锁)a)b)   

  1. a Department of Physics, Liaocheng University, Liaocheng 252059, China; b Department of Physics, Liaocheng University, Liaocheng 252059, China;Department of Physics, Qufu Normal University, Qufu 273165, China
  • Revised:2010-01-18 Online:2010-07-15 Published:2010-07-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10574060), the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23) and the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07).

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摘要： Noticing that the equation frac
d2On
dt2={Hc,{Hc,On}} =λOn with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Lett. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invariant eigen-operator method.

Abstract: Noticing that the equation $\frac{ d ^{2} O_{ n }}{ d t^{2}}=\{H_{ c },\{H_{ c }, O_{ n }\}\}=\lambda O_{ n }$  with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Lett. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invariant eigen-operator method.

Key words: quantum impeller, vibration spectrum, invariant eigen-operator method

中图分类号:  (Phonons in crystal lattices)

  • 63.20.-e
03.65.Fd (Algebraic methods) 02.10.Ud (Linear algebra) 02.30.Hq (Ordinary differential equations)