Ys. Li et Js. He, EXACT SOLUTION OF THE SCHRODINGER-EQUATION FOR THE TIME-DEPENDENT HARMONIC-OSCILLATOR, Chinese Science Bulletin, 43(13), 1998, pp. 1066-1071
By using the soliton theory, it is known that the exact solutions of t
he Schrodinger equation for the time-dependent harmonic oscillator onl
y need to solve an oscillation equation with respect to space variable
and a time-dependent Schrodinger equation.