量子N体系统的广义径向方程  

Generalized Radial Equations for a Quantum N-body System

作　　者：马中骐[1] 段斌[1] 顾晓艳[1] 

机构地区：[1]中国科学院高能物理研究所,北京100039

出　　处：《原子核物理评论》2001年第4期261-265,共5页Nuclear Physics Review

基　　金：国家自然科学基金资助项目 ( 10 0 75 0 5 0 ) ;博士后科学基金资助项目~~

摘　　要：介绍一种精确的方法 ,在质心坐标系中 ,把量子 N体系统的整体转动自由度和内部运动自由度完全地分离开来 .对于确定的轨道角动量状态 ,找到了一组完备且独立的角动量本征函数基 ,它们是坐标分量的齐次多项式 ,且满足 Laplace方程 .系统中的任何角动量本征函数都可以用这组函数基展开 ,组合系数只依赖于内部变量 ,称为广义径向函数 .可以简单且明显地推导出广义径向函数所满足的广义径向方程 .函数和方程式都只依赖于 (3 N- 6 )个内部变量 ,而且个数是有限的 .A method without any approximation to separate the global rotational degrees of freedom in the Schrdinger equation for an N -body system completely from the internal ones is presented. For given orbital angular momentum states, we discover a complete set of independent base-functions, which are homogeneous polynomials in the components of the coordinate vectors and satisfy the Laplace equation. Any function with the given angular momentum and the given parity in the system can be expanded with respect to the base-functions, where the coefficients are the functions of the internal variables, called the generalized radial functions. We explicitly establish the simultaneous equations with the finite number for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations.

关 键 词：量子N体系统 薛定谔方程 广义径向方程 质心坐标系 广义径向函数 整体转自由度 原子 角动量本征函数基 

分 类 号：O562.1[理学—原子与分子物理] O413[理学—物理]