Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator

CHENG Yan-Fu; DAI Tong-Qing

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2006, Vol. 30> Issue(10) : 944-949

Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator

CHENG Yan-Fu ^, ,
DAI Tong-Qing

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

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Abstract：
Classical and quantum oscillator of generalized anharmonicity is solved analytically up to the linear power of ε by using the multiple-scale perturbation method. The commutation relation of position and momentum operator can be simplified easily and the quantum solutions transformed into the classical form conveniently under the extreme conditions, which are different from the earlier multiple-scale perturbation theory. Moreover compared with the Taylor series solution, the frequency shifts in our solutions appear in the expression of oscillations of all orders in both classical and quantum cases, so multiple-scale perturbation method is more suitable for solving the weak-coupling anharmonic oscillation than the Taylor series approach.

References

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. Nayfeh A H. Introduction to Perturbation Techniques. NewYok: Wikey, 19812. Fernandez F M. Introduction to Perturbation Theory inQuantum Mechanics. Noca Ratom: CRC Press, 20003. Bender C M, Bettencourt L M A. Phys. Rev., 1996, D54: 77104. Bender C M, Bettencourt L M A. Phys. Rev. Lett., 1996,54: 41145. Auberson G, Capdequi P M. Phys. Rev., 2002, A65: 16. Pathak A, Mandal S. Phys. Lett., 2001, 286: 2617. Pathak A, Mandal S. Phys. Lett., 2002, 298: 2598. CHENG Yan-Fu, DAI Tong-Qing. HEP NP, 2006, 30(6): 513(in Chinese)(程衍富, 戴同庆. 高能物理与核物理, 2006, 30(6): 513)

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CHENG Yan-Fu and DAI Tong-Qing. Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator[J]. Chinese Physics C, 2006, 30(10): 944-949.

CHENG Yan-Fu and DAI Tong-Qing. Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator[J]. Chinese Physics C, 2006, 30(10): 944-949. shu

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Received: 2006-02-27
Revised: 2006-03-18

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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 Generalized Anharmonic Oscillator

CHENG Yan-Fu ^,
DAI Tong-Qing

Corresponding author: CHENG Yan-Fu,

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

Received Date: 2006-02-27
Accepted Date: 2006-03-18
Available Online: 2006-10-05

Abstract: Classical and quantum oscillator of generalized anharmonicity is solved analytically up to the linear power of ε by using the multiple-scale perturbation method. The commutation relation of position and momentum operator can be simplified easily and the quantum solutions transformed into the classical form conveniently under the extreme conditions, which are different from the earlier multiple-scale perturbation theory. Moreover compared with the Taylor series solution, the frequency shifts in our solutions appear in the expression of oscillations of all orders in both classical and quantum cases, so multiple-scale perturbation method is more suitable for solving the weak-coupling anharmonic oscillation than the Taylor series approach.