Modification of Bertrand’s Theorem and Extended Runge-Lenz Vector

Chin. Phys. Lett.

1999, Vol. 16

Issue (11): 781-783 DOI:

Original Articles

Modification of Bertrand’s Theorem and Extended Runge-Lenz Vector

WU Zuo-bing^1,2;ZENG Jin-yan¹

¹Department of Physics, Peking University, Beijing 100871 ²Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080

Cite this article:

WU Zuo-bing, ZENG Jin-yan 1999 Chin. Phys. Lett. 16 781-783

Download: PDF(210KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract It is shown that for a particle with suitable angular momenta in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O₃. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

Keywords: 03.65.-w 03.65.Ge

Published: 01 November 1999

PACS:	03.65.-w	(Quantum mechanics)
	03.65.Ge	(Solutions of wave equations: bound states)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/ OR https://cpl.iphy.ac.cn/Y1999/V16/I11/0781

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	WU Zuo-bing
	ZENG Jin-yan

Related articles from Frontiers Journals

[1]	Ramesh Kumar, Fakir Chand. Energy Spectra of the Coulomb Perturbed Potential in N-Dimensional Hilbert Space[J]. Chin. Phys. Lett., 2012, 29(6): 781-783
[2]	Akpan N. Ikot. Solutions to the Klein–Gordon Equation with Equal Scalar and Vector Modified Hylleraas Plus Exponential Rosen Morse Potentials[J]. Chin. Phys. Lett., 2012, 29(6): 781-783
[3]	NIU Yao-Bin, WANG Zhong-Wei, DONG Si-Wei. Modified Homotopy Perturbation Method for Certain Strongly Nonlinear Oscillators[J]. Chin. Phys. Lett., 2012, 29(6): 781-783
[4]	ZHOU Jun,SONG Jun,YUAN Hao,ZHANG Bo. The Statistical Properties of a New Type of Photon-Subtracted Squeezed Coherent State[J]. Chin. Phys. Lett., 2012, 29(5): 781-783
[5]	A. I. Arbab. Transport Properties of the Universal Quantum Equation[J]. Chin. Phys. Lett., 2012, 29(3): 781-783
[6]	Ahmad Nawaz. Quantum State Tomography and Quantum Games[J]. Chin. Phys. Lett., 2012, 29(3): 781-783
[7]	WANG Jun-Min. Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation[J]. Chin. Phys. Lett., 2012, 29(2): 781-783
[8]	Hassanabadi Hassan, Yazarloo Bentol Hoda, LU Liang-Liang. Approximate Analytical Solutions to the Generalized Pöschl–Teller Potential in D Dimensions[J]. Chin. Phys. Lett., 2012, 29(2): 781-783
[9]	ZHAI Zhi-Yuan, YANG Tao, PAN Xiao-Yin. Exact Propagator for the Anisotropic Two-Dimensional Charged Harmonic Oscillator in a Constant Magnetic Field and an Arbitrary Electric Field**[J]. Chin. Phys. Lett., 2012, 29(1): 781-783
[10]	Ciprian Dariescu, Marina-Aura Dariescu. Chiral Fermion Conductivity in Graphene-Like Samples Subjected to Orthogonal Fields**[J]. Chin. Phys. Lett., 2012, 29(1): 781-783
[11]	CHEN Qing-Hu, , LI Lei, LIU Tao, WANG Ke-Lin. The Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime**[J]. Chin. Phys. Lett., 2012, 29(1): 781-783
[12]	WANG Jun-Min, YANG Xiao . Theta-function Solutions to the (2+1)-Dimensional Breaking Soliton Equation**[J]. Chin. Phys. Lett., 2011, 28(9): 781-783
[13]	M. R. Setare, , D. Jahani, * . Quantum Hall Effect and Different Zero-Energy Modes of Graphene[J]. Chin. Phys. Lett., 2011, 28(9): 781-783
[14]	S. Ali Shan, , A. Mushtaq . Role of Jeans Instability in Multi-Component Quantum Plasmas in the Presence of Fermi Pressure**[J]. Chin. Phys. Lett., 2011, 28(7): 781-783
[15]	ZHANG Xue, ZHENG Tai-Yu, TIAN Tian, PAN Shu-Mei . The Dynamical Casimir Effect versus Collective Excitations in Atom Ensemble[J]. Chin. Phys. Lett., 2011, 28(6): 781-783

Viewed

Full text

Abstract