Based on the model inducing the inverse square potential function non-harmonics oscillator,in the coordinates representation,precisely solved the energy eigen equation which this kind of harmonic oscillator complies with,did to the non-resonant parameter and the energy level formula discussed quite thoroughly.
By the Fourier transform ation,we change the Schr dinger equation of one-dimensional linear harmonic oscillator to the first-order differential equation which can be easily solved.The progressional solution of the Schr dinger equation can be obtained by the inverse Fourier transform ation after we solve the first-order differential equation.Finally,we can fix the eigen-value and eigen-function of energy based on the boundary condition that wave function is zero when the variable becomes infinite.