A method to obtain the solution of the time- independent Schrodinger equation for the simple harmonic oscillator

A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial solution into the same equation, an equation of that unknown function is obtained. This equation has a recursive property which has been exploited to obtain the solutions of the equation. It is all about reconstruction of the equation with different solutions of that unknown function by repetitive differentiation and that ultimately leads to the wave functions of the Schrodinger equation for harmonic oscillator.