幂函数叠加势的径向薛定谔方程的解析解

摘要

When Schr(o)dinger equation appears high power and inverse power potential function or the superposed potential function which are the high order inharmonic oscillator potential,the electric dipole moment potential,the molecular crystal potential,the polarized equivalent potential and the solution process of the Schr? dinger equation is very complex.In this paper,the combination of solution method of series and asymptotic solution are utilized near singular points,a series analytic solution of the wave functions of stationary state for radial Schr(o)dinger equation with potential function V(r)=a1r6+a2r2+a3r-4+a4r-6 and the corresponding energy level structure are obtained by the comparative method of the coefficient,meanwhile,proper discussion and some important conclusions are presented in this paper.%当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,本文采用奇点邻域附近的级数解法与求解渐近解相结合并且通过系数比较法,得到势函数为V(r)=a1r6+a2r2+a3r-4+a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构,并作了适当讨论与结论.