论文标题
具有标量和矢量电势的Schroedinger方程的对称性
Symmetries of Schroedinger equation with scalar and vector potentials
论文作者
论文摘要
使用代数方法将与标量和矢量势相互作用的带电粒子相互作用的时间依赖的Schroedinger方程的对称性进行分类。也就是说，所有的不相等方程式都呈现了相对于连续转换组的对称转换。此分类已完成，包括对对称性的规范和此类方程式的可接受的等效关系。特别是，发现了自由施罗丁格方程与排斥振荡器之间的简单映射，具有清晰的群体理论意义。
Using the algebraic approach Lie symmetries of time dependent Schroedinger equations for charged particles interacting with superpositions of scalar and vector potentials are classified. Namely, all the inequivalent equations admitting symmetry transformations with respect to continuous groups of transformations are presented. This classification is completed and includes the specification of symmetries and admissible equivalence relations for such equations. In particular, a simple mapping between the free Schroedinger equation and the repulsive oscillator is found which has a clear group-theoretical sense.
