Abstract: The one-dimensional classical forced oscillator is quantized.The exact solution of time evolution operator of the system is obtained.The quasi-probability distribution function of phase space is used to investigate the quantum characteristics of one-dimensional forced oscillator.The results show that the Wigner function is two-dimensional Gaussian wave packet from the initial vacuum state.The central coordinate and momentum of the Gaussian wave packet move in the same manner as one-dimensional classical harmonic oscillator.The amplitude and phase of the centre of the wave packet are modulated by the force.

Key words: one-dimensional forced oscillator, coherent state, quasi-probability distribution functions of phase space