| Analytic solution and approximate solution for solving the Schr?dinger equation are presented . And the radial Schr?dinger equation with the high order power and inverse power potential function or the superposed potential function which are the high order anharmonic oscillator potential is studied. For a given form of high order power and inverse power potential, firstly,we study the limiting form of equation as r→0and as r→∞to obtain a convenient factorization of its solution for all values of r. Secondly, using the contimued fraction method ,an analytic solution of the superposition potential with the power and the invers-power potential V ( r)= a1r6 +a2r2+a3r?4 +a4r?6 has been obtened and some conclusions are presented. The radial wave function of Schr?dinger equation for the power and the invers-power potential can be written in the form of a product of an exponential function and a polynomial function . The exact energy and wave function of the potential are obtained by using the relation for the coefficient of the polynomial function. In the bound states ,the results show that parameters in the model potential have to satisfy relevant restraint conditions.Many efforts have been produced in the literature over several decades to study the stationary Schr?dinger equation in various dimensions with a central potential containing negative powers of the radial coordinate. For the reasons described, we are interested in a potential V having the form with the power and the invers-power potential .The bound states of Klein-Gordon equation of the power and the invers-power potential with equal scalar and vector potentials are solved. The exact energy spectrum equations and the wave function are obtained.For a three-dimensional non-harmonic oscillator potential V = 1/ 2 r 2 + A / r 2 + B / r 4 + C /r6,the s-wave bound solutions of an Klein-Gordon equation are given when the scalar potential is equal to the vector potential .
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