双环形氢原子势束缚态的精确解  

Exact Bound State Solutions of the Double Ring-shaped Hydrogen Potential

作　　者：柏于杰[1] 

机构地区：[1]盐城工学院基础教学部,江苏盐城224051

出　　处：《盐城工学院学报（自然科学版）》2009年第4期13-16,共4页Journal of Yancheng Institute of Technology:Natural Science Edition

摘　　要：若氢原子势被一个双环形状的平方反比势环绕,即称为双环形氢原子势。采用解析方法研究了双环形氢原子势束缚态的精确解,首先将双环形氢原子势的Schrdinger方程在球坐标系中进行分离变量,然后利用超几何方程和合流超几何方程求解角向方程和径向方程,给出了精确的能谱方程,获得了用超几何函数表示的归一化的角向波函数和用拉革尔多项式表示的归一化径向波函数。If the hydrogen potential is surrounded by double ring - shaped inversed square potential, it is defined as double ring - shaped hydrogen potential. This paper deals with the bound state exact solutions of double ring - shaped hydrogen potential with interpreting method. First, the Schrodinger equation of double ring - shaped hydrogen potential is solved in spherical polar coor- dinates by adopting the variable separation. Then the angular and radial functions are handled respectively by using the hyper ge- ometric equation and the confluent hyper geometric equation, therefore the exact energy spectrum is obtained. The normalized an- gular wave functions expressed in terms of the standard hyper geometric function and the normalized radial wave functions expressed by means of the Lagurre polynomials are presented.

关 键 词：双环形氢原子势 Schrdinger方程 束缚态 精确解 

分 类 号：O413.1[理学—理论物理]