用Laplace变换求Hartmann势的精确解及波函数的递推关系  

Exact solution of the Hartmann potential and the recursion relat ions of wave function via Laplace transforms

作　　者：陈子栋[1] 

机构地区：[1]绍兴文理学院物理系,绍兴312000

出　　处：《原子与分子物理学报》2005年第3期483-487,共5页Journal of Atomic and Molecular Physics

摘　　要：本文求解了在球坐标下Hartmann势的Schrdinger方程,得到了能量方程和归一化的波函数。用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数。讨论了径向本征函数的像函数的递推关系,从而得出径向波函数的递推关系。In this paper, We solved the Schr（oe）dinger equation with Hartmann potential in spherical polar coordinates and gave the exact energy equation and the normalized wave function. The second-order radial differential equation is reduced to a first-order differential equation by means of the Laplace transform, and then, its solutions are obtained by integral directly. To get the required eigenfunction employed the expansions of series and inverse Laplace transform. The recursion relation of the mirror function of radial eigenfunctions is discussed, and the recursion relation of radial wave function is obtained.

关 键 词：HARTMANN势 Schr(oe)dinger方程 LAPLACE变换 归一化波函数 递推关系 

分 类 号：O413.1[理学—理论物理]