研究表明，保证经典轨道具有封闭性的Bertrand定理可以进一步推广，在适当的角动量下，仍存在着非椭圆的闭合轨道．对于屏蔽Coulomb场，可获得广义Runge-Lenz矢量．这种轨道封闭性与径向Schr?dinger方程因式分解相对应．
It is shown that for a particle with suitable angular momenta in the screened Coulomb poten-tial or isotropic harmonic potential, there still exists closed orbits rather than ellipse, characterized by theconserved perihelion and aphelion vectors, i.e. , extended Runge-Lenz vector, Which implies a higher dy-namical symmetry than the geometrical symmetry SO3. For the potential, factorization of the radialSchrodinger equation to produce raising and lowering operators is also pointed out.
参考文献
| [1] | Goldstein H. Classical Mechanics, 2nd ed. Addison-Wesley,New York, 1980. |
| [2] | DeLange O L, Raab R E. Operator Methods in Quantum Mechanics. Clarendon, Oxford, 1991. |
| [3] | Cooper F, Khare A, Sukhatme U P. Supersymmetry and Quantum Mechanics. Phys Rep, 1995, 251: 267～385. |
| [4] | Liu Y F, Lei Y A, Zeng J Y. Factorization of the Radial Schrodinger Equation and Four Kinds of Raising and Lowering Operators of Hydrogen Atoms and Isotropic Harmonic Oscillators. Phys Lett, 1997, A231: 9～12. |
| [5] | Runge C. Vektoranalyses. Hirzel, Leipzig, 1919, 1: 70; Lenz W. Uber den Bewegungsverlauf und die Quantenzustande der Gestorten Keplerbewegung. Z Phys, i924, 24: 197～207;Laplace P S. Traite de Mechnique Celeste. Villars, Paris,1799, I. |
| [6] | Pauli W. Uber das Wasserstroffspektrum yom Standpunkt der Neuen Quantenmechanik. Z Phys, 1926, 36: 336～363. |
| [7] | 曾谨言．量子力学．卷二，北京：科学出版社，1997． |
| [8] | Liu Y F, Huo W J, Zeng J Y. Connection between the Closeness of Classical Orbits and Factorization of the Radial Schrddinger Equation. Phys Rev, 1998, A58: 852～868. |
| [9] | Wu Z B, Zeng J Y. Extension of Bertrand's Theorem and Factorization of the Radial Schrodinger Equation. J Math Phys,1998, 39：5 253～5 259. |
| [10] | Wu Z B, Zeng J Y. Modification of Bertrand′s Theorem and Extended Runge-Lenz Vector. Chin Phys Lett, 1999, 16：781～783. |
| [11] | Quigg C, Rosner J L. Quantum Mechanics with Application to Quarkonium. Phys Rep, 1979, 56: 167～235. |
| [12] | 钱伯初，曾谨言．量子力学习题精选解析．北京：科学出版社，1990． |
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