Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator

CHENG Yan-Fu; DAI Tong-Qing

Chinese Physics C> 2006, Vol. 30> Issue(6) : 513-516

Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator

CHENG Yan-Fu ^, ,
DAI Tong-Qing

College of Electronic Information Engineering, South-Central University for Nationalities, Wuhan 430074, China

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Abstract：
Classical and quantum oscillators of sextic anharmonicity are analytically solved up to the n-th power of ε(weak-coupling constant) by using the multiple-scale perturbation theory. Differing from Taylor series solution, the frequency shift appears in all orders of oscillations no matter it is in the classical or quantum case. So the multiple-scale perturbation theory is an approximate method to deal with the weak-coupled anharmonic oscillation and is better than the Taylor series approach.

References

[1]

. Nayfeh A H. Introduction to Perturbation Techniques. New York: Wiley, 19812. Mandal S. J. Phys., 1998, A31: L5013. Bender C M, Bettencourt M A. Phys. Rev. Lett., 1996, 77:41144. Bender C M, Bettencourt M A. Phys. Rev., 1996, D54:77105. Pathak A, Mandal S. Phys. Lett., 2001, A261:2766. Auberson G, Capdequi P M. Phys. Rev., 2002, A65: 17. Pathak A, Mandal S. Phys. Lett., 2002, A298: 2598. Janowicz M. Phys. Rrp., 2003, 375: 3279. Kahn P B, Zarmi Y. Amer. J. Phys., 2004, 72: 538

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CHENG Yan-Fu and DAI Tong-Qing. Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator[J]. Chinese Physics C, 2006, 30(6): 513-516.

CHENG Yan-Fu and DAI Tong-Qing. Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator[J]. Chinese Physics C, 2006, 30(6): 513-516. shu

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Received: 2005-08-23
Revised: 2005-12-04

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沈阳化工大学材料科学与工程学院沈阳 110142

Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator

CHENG Yan-Fu ^,
DAI Tong-Qing

Corresponding author: CHENG Yan-Fu,

College of Electronic Information Engineering, South-Central University for Nationalities, Wuhan 430074, China

Received Date: 2005-08-23
Accepted Date: 2005-12-04
Available Online: 2006-06-05

Abstract: Classical and quantum oscillators of sextic anharmonicity are analytically solved up to the n-th power of ε(weak-coupling constant) by using the multiple-scale perturbation theory. Differing from Taylor series solution, the frequency shift appears in all orders of oscillations no matter it is in the classical or quantum case. So the multiple-scale perturbation theory is an approximate method to deal with the weak-coupled anharmonic oscillation and is better than the Taylor series approach.