二维各向同性谐振子的径向矩阵元计算的讨论  

Discussion on Calculation of Radial Matrix Elements of Two-dimensional Isotropic Oscillator

作　　者：狄尧民[1] 刘思平[1] 刘莉[1] 程阳[1] 解霞[1] 

机构地区：[1]徐州师范大学物理系,江苏徐州221116

出　　处：《量子光学学报》2004年第2期59-61,共3页Journal of Quantum Optics

基　　金：徐州师范大学科研基金(重点项目)

摘　　要：根据广义Laguerre多项式的数学性质,导出了较为简单的二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ρ整数次幂的平均值,电偶极跃迁矩阵元和电四极跃迁矩阵元。A concise general formula of the radial matrix element of the two-dimensional isotropic oscillator is derived by use of the properties of the generalized 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：二维各向同性谐振子 径向矩阵元 广义Laguerre多项式 偶极跃迁 四极跃迁 

分 类 号：O431[机械工程—光学工程]