Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator

  • 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.
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  • [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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Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator

    Corresponding author: CHENG Yan-Fu,
  • College of Electronic Information Engineering, South-Central University for Nationalities, Wuhan 430074, China

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.

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