Abstract: The evolution of one-dimensional free particle is calculated by using time-evolution operator. The evolution of the variance of one-dimensional free particle wave packet is calculated，the results show that the wave packet spreads over time. Using the annihilation operator，the evolution of wave function of Gaussian wave packet is calculated，here the Gaussian wave packet is a“stationary”wave packet located at the origin at the initial time. A series expression is obtained，sum it up the elementary function expression is obtained，the spreading of the wave packet in time has been directly confirmed.

Key words: time-evolution operator, free particle, propagation of wave packet