Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator

WANG Peng; WANG Shun-Jin

Chinese Physics C> 2005, Vol. 29> Issue(7) : 651-656

Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator

WANG Peng ,
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

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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.

References

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. 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

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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

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Received: 2004-09-04
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator

WANG Peng
WANG Shun-Jin ^,

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

Received Date: 2004-09-04
Accepted Date: 1900-01-01
Available Online: 2005-07-05

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.