用Laplace变换求Kratzer势径向波函数的二类递推关系

摘要

求解了Kratzer势的Schr(o)dinger方程,得到了归一化的波函数和能量方程.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.另外,用Laplace变换方法给出了径向波函数关于量子数N和角量子数L的二类递推关系.%In this paper the exact bound state solutions including the energy equation and normalized wave function of Schrdinger equation with the Kratzer potential is obtained.By using the Laplace transformation this second-order differential equation can be reduced to the first-order case and then the eigenfunction can be derived from direct integral and a simple series expansion via Laplace inverse transform.In addition,two kinds of recursive relations about the principle and angular quantum numbers N and L for the radial wave function are also given by using the same method.