经典轨道的封闭性和径向Schr?dinger方程的因式分解

武作兵; 曾谨言

doi:10.3969/j.issn.1007-4627.2000.01.008

原子核物理评论

经典轨道的封闭性和径向Schr?dinger方程的因式分解

武作兵, 曾谨言. 2000: 经典轨道的封闭性和径向Schr?dinger方程的因式分解, 原子核物理评论, 17(1): 35-38. doi: 10.3969/j.issn.1007-4627.2000.01.008

引用本文:

武作兵, 曾谨言. 2000: 经典轨道的封闭性和径向Schr?dinger方程的因式分解, 原子核物理评论, 17(1): 35-38. doi: 10.3969/j.issn.1007-4627.2000.01.008

2000: Closeness of Classical Orbits and Factorization of Radial Schrodinger Equation, Nuclear Physics Review, 17(1): 35-38. doi: 10.3969/j.issn.1007-4627.2000.01.008

Citation:

2000: Closeness of Classical Orbits and Factorization of Radial Schrodinger Equation, Nuclear Physics Review, 17(1): 35-38. doi: 10.3969/j.issn.1007-4627.2000.01.008

经典轨道的封闭性和径向Schr?dinger方程的因式分解

北京大学物理系，北京 100871;中国科学院力学研究所非线性力学国家重点实验室，北京 100080
北京大学物理系，北京 100871

Closeness of Classical Orbits and Factorization of Radial Schrodinger Equation

摘要: 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．
- Bertrand定理 /
- 闭合轨道 /
- 升降算子
Abstract: 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.