利用基矢变换法求解轨道角动量算符在球坐标系中的表示

Solving the Expression of Orbital Angular Momentum Operator in Spherical Coordinate System by Basis Transformation

力学量算符理论是量子力学的核心内容之一,而轨道角动量又是非常重要的力学量。该文巧妙地利用基矢变换法求出了轨道角动量算符及轨道角动量的三个分量算符在球坐标系中的表示形式,进而用两种方法导出了轨道角动量平方算符在球坐标系中的表示。与传统方法相比,文中的新方法不仅可以简化推导过程、节省教学时间,而且通俗易懂,更容易被接受。该方法在教学实践中已收到良好的反响。

The theory of observables operator is one of the core contents of quantum mechanics,and orbital angular momentum is one of the very important observables.In this paper,the expressions of orbital angular momentum operator and its three components in spherical coordinate system are obtained by using the method of basis transformation.And then the expression of orbital angular momentum square operator in spherical coordinate system is also derived by two methods.Compared with the traditional method,the new method in this paper can not only simplify the derivation process,save teaching time,but also be easy to be understood and accepted.The aforementioned methods have received a good response in teaching practice.