中文摘要：

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,采用奇点邻域附近的级数解法与求解渐近解相结合,在多种相互作用幂函数紧密耦合的条件下,得到势函数为V（r）=a1r^6＋a2r^2＋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.

英文摘要：

When the Schrdinger equation involves high-order power and inverse power potential functions or the superposed potential function of high-order anharmonic oscillatory potentials, introduced by the presence of electric dipole moment potential, molecular crystal potential, or the polarized equivalent potential, the solution of the Schrdinger equation becomes very complicated. In this paper, with the help of a combination of series solutions and asymptotic solutions utilized near the singular points, a series analytic solution of the wave functions of stationary state for radial Schrdinger equation with potential function V（r） =a1r^6＋a2r^2＋a3r^-4 ＋a4r^-6 and the corresponding energy level structure are obtained under the tightly-coupled condition of the interacting power potential functions. Meanwhile, the paper gives a proper discussion and some important conclusions are drawn.