用Laplace变换求Hartmann势的精确解及波函数的递推关系

本文求解了在球坐标下Hartmann势的Schrdinger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.

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

In this paper, We solved the Schrdinger equation with Hartmann potential in sp herical polar coordinates and gave the exact energy equation and the normalized wave function. The second-order radial differential equation is reduced to a f ir st-order differential equation by means of the Laplace transform, and then, its solutions are obtained by integral directly. To get the required eigenf unction employed the expansions of series and inverse Laplace transform. The re cursion relation of the mirror function of radial eigenfunctions is discussed, and the recursion relation of radial wave function is obtained