Abstract: Many physical systems can be described by oscillator with time-dependent mass and frequency. Investigation

and solution of time-dependent system are very important in quantum field as well as in quantum optics.

We use SU( 1，1) Lie-algebraic technique to investigate the harmonic oscillator with time-dependent mass and frequency

and obtain the time evolution operator by solving Riccati equation. Than the formula of the system is derived

in phase space. Finally，we obtain the propagator of oscillator of the free particle，driven by gravity，period mass

　　and damped system.

Key words: forced oscillator, Riccati equation, SU( 1, 1) Lie-algebraic, propagator