关于三维各向同性谐振子径向矩阵元计算的讨论  

Discussion on the calculation of radial matrix elements of three-dimensional isotropic oscillator

作　　者：狄尧民[1] 

机构地区：[1]徐州师范大学物理系,徐州221009

出　　处：《物理学报》2003年第4期786-789,共4页Acta Physica Sinica

基　　金：江苏省教育厅自然科学基金资助的课题~~

摘　　要：根据广义Laguerre多项式的数学性质 ,导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式 ,并在这基础上计算了一些重要特殊情形的径向矩阵元 :矢径r整数次幂的平均值 。A concise general formula of the radial matrix element of the three-dimensional isotropic oscillator is derived using the properties of the general Laguerre polynomials. Some important special cases, such as the average value of the integer power of radial vector, the matrix element of the electric dipole transition and the element of the electric quadrupole transition, are obtained from the general formula.

关 键 词：三维各向同性谐振子 径向矩阵元 量子力学 计算 广义Laguerre多项式 电偶极跃迁 电四极跃迁 

分 类 号：O413.1[理学—理论物理]