Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator

  • One-dimensional time-dependent classical harmonic oscillator is a nonautonomous system with an SU(1,1) dynamical symmetry. By means of algebraic dynamics method, we have obtained its exact solution for the first time. As the time-dependent stiffness of the harmonic oscillator assumes some elementary functions, such as power functions, trigonal functions, exponential functions etc., the exact solutions become analytic. The recently proposed "analytic approximation solution" is proved to be a good approximation to the corresponding analytic solution under some conditions.
  • 加载中
  • [1] . Freer M,Betts R R. Nucl . Phys. , 1995 , A587 : 36 ; Dong Y B ,Faessler A. Nucl . Phys. , 1999 , A651 :2092. Paul W. Rev. Mod. Phys. , 1990 , 62 :531 ; Brown L S. Phys. Rev.Lett . , 1991 , 66 :5273. Colegrave R K, Abdallas M S. Opt . Acta , 1981 , 28 :4954. WANG S J , ZUO W. Phys. Lett . , 1994 , A196 :135. ZUO W, WANG S J . Acta Physica Sinica , 1995 , 44(8) :11776. Guasti F M. Physica , 2004 , D189 :1887. WANG S J , LI F L , Weiguny A. Phys. Lett . , 1994 , A180 :189
  • 加载中

Get Citation
WANG Peng and WANG Shun-Jin. Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator[J]. Chinese Physics C, 2005, 29(7): 651-656.
WANG Peng and WANG Shun-Jin. Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator[J]. Chinese Physics C, 2005, 29(7): 651-656. shu
Milestone
Received: 2004-09-04
Revised: 1900-01-01
Article Metric

Article Views(2734)
PDF Downloads(563)
Cited by(0)
Policy on re-use
To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator

    Corresponding author: WANG Shun-Jin,
  • Department of Physics,Sichuan University,Chengdu 610064,China2 Institute of Physics,Southwest Jiaotong University,Chengdu 610031,China3 Nuclear Theory Center of HIRFL,Lanzhou 730000,China

Abstract: One-dimensional time-dependent classical harmonic oscillator is a nonautonomous system with an SU(1,1) dynamical symmetry. By means of algebraic dynamics method, we have obtained its exact solution for the first time. As the time-dependent stiffness of the harmonic oscillator assumes some elementary functions, such as power functions, trigonal functions, exponential functions etc., the exact solutions become analytic. The recently proposed "analytic approximation solution" is proved to be a good approximation to the corresponding analytic solution under some conditions.

    HTML

Reference (1)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return