›› 2015, Vol. 34 ›› Issue (10): 5-5.

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  1. 暨南大学理工学院物理系,广东广州510632
  • 出版日期:2015-10-25 发布日期:2015-10-20

A brief review on Laplace-Runge-Lenz vector

  • Online:2015-10-25 Published:2015-10-20

摘要: 介绍了拉普拉斯-隆格-楞次矢量在经典力学、广义相对论以及量子力学中的应用.利用该矢量在经典和量子开普勒问题中的守恒性,可以不求解运动方程而直接得到系统的重要性质,如轨道方程、能量本征值等;广义相对论对牛顿引力的修正会破坏该矢量的守恒性,而它随时间的演化方程,也可以完全决定轨道进动角和光线在引力场中的偏移.这些都说明,拉普拉斯-隆格-楞次矢量是反应系统动力学对称性的一个基本物理量,将其引入大学物理教学是十分有意义的.

关键词: 拉普拉斯-隆格-楞次矢量, 开普勒问题, 近日点进动, 光线弯曲, 氢原子能级

Abstract: Applications of Laplace- Runge-Lenz vector in classical mechanics, quantum mechanics and general relativity are reviewed briefly. By using this vector conserved in classical and quantum Kepler problems, one can study some important properties, such as obit equation and eigenvalue of energy, without solving the equa- tions of motion. Although the corrections from general relativity violate the conservation, its evolution, with respect to time, will completely determine the perihelion precession and light bending. All these examples indicate that La- place-Runge-Lenz vector is a fundamental physics quantity which is dictated by basic dynamical symmetries, thus it is instructive to introduce it into general physics courses.

Key words: Laplace- Runge- Lenz vector, Kepler problem, perihelion precession, light bending, hydrogenenergy levels


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