类氢原子薛定谔方程解析解的进一步研究  

Further Study on the Analytical Solution of Schr dinger Equation of a Hydrogen-Like Atom

作　　者：张中良[1] 张武寿[1] 张兆群[2] 

机构地区：[1]中国科学院化学研究所,北京100080 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《中国科学院研究生院学报》2002年第2期186-191,共6页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：国家自然科学基金资助课题(10 14 5 0 0 6)

摘　　要：在以往工作基础上对类氢原子体系的薛定谔方程进行了进一步求解。若不忽略r-n因子,可以获得该方程的三组解析解:一组与传统类氢原子波函数相同;一组发散;另一组与传统径向波函数完全不同。由于考虑到原子核有一定的大小(size),最后一组径向波函数不随r趋于零而发散。该组径向波函数至少有如下显著特点:(1 )角量子数l必须大于主量子数n;(2)l不能为 0和 1;(3)与它相对应的电子云分布不同于传统的结果;(4)其电子云密度与相应传统结果比较,更靠近原子核。此外,其结果主要由数学推导结合某些物理考虑得出,其有效性还需要实验验证。Based on the previous works, the Schrdinger equation of the hydrogen-like atom is analytically solved further. Three sets of analytical solutions are obtained if the factor r~ -nis not neglected. The first solution is the same as the traditional radial wave function, the second diverges, and the last one is quite different from the traditional solution. On the consideration of the finite size of the nuclear, the third wave function does not diverge when r approaches to zero. Its radial wave function has the following characteristics: (1) the angular-momentum quantum number l must be greater than the principal quantum number n; (2) l must not be 0 or 1; (3) the electron-cloud distribution differs from the traditional one; (4) the electron is closer to the nuclear than that in traditional results. On the other hand, the validity of solutions needs to be verified experimentally.

关 键 词：类氢原子 薛定谔方程 解析解 量子力学 径向波函数 电子云密度 

分 类 号：O413.1[理学—理论物理]