文献类型：期刊文献

中文题名：均匀磁场中二维各向同性带电谐振子的守恒量与对称性研究

英文题名：The study of conserved quantities and symmetries for two-dimensional isotropic harmonic charged oscillator moving in homogeneous magnetic field

作者：楼智美[1]

机构：[1]绍兴文理学院物理系

年份：2013

期号：22

起止页码：1

中文期刊名：物理学报

外文期刊名：Acta Physica Sinica

收录：SCI-EXPANDED(收录号：WOS:000327815700001)、CSTPCD、、北大核心2011、EI(收录号：20134917048400)、Scopus(收录号：2-s2.0-84888325097)、WOS、北大核心、CSCD、CSCD2013_2014

基金：Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10932002)

语种：中文

中文关键词：二维各向同性带电谐振子;守恒量;Noether对称性;Lie对称性

外文关键词：two-dimensional isotropic harmonic charged oscillator, conserved quantities, Noether symmetries, Liesymmetries

中文摘要：由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程.

外文摘要：The kinematic differentiation equations of two-dimensional isotropic harmonic charged oscillator moving in a homogeneous magnetic are obtained by using Newton＇s second law. Two integrals （conserved quantities） are obtained by directly integrating the kinematic differentiation equations. The relationship between the Lagrangian and the conserved quantity is established through the Legendre transformation, thereby obtaining a Lagrangian function of the system. The Noether symmetry and Lie symmetry of the infinitesimal transformations corresponding to the conserved quantities are studied. Finally, the kinematical equations of the system are obtained.