When the Schrdinger 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 Schrdinger 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 Schrdinger equation with potential function V(r)=a1r6+a2r2+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.
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