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

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.

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

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.
Keywords：two-dimensional isotropic harmonic charged oscillatorconserved quantitiesNoether symmetriesLie symmetries