Abstract: Combined with the Airy function and its basis properties，this article studies the microscopic motion of a wave packet of a particle in a linear potential field. The Schrdinger equations for the linear potential and the V potential are solved to give the wave functions and the energy level structure of the particle. Then，in the free space，the free motion of Airy package is investigated in detail. The calculation reveals that a free Airy wave packet shows a self-acceleration in the free space. Finally，some experiments to show the strange evolution of Airy wave　packet are demonstrated.

Key words: Airy function, Fourier transformation, Schrdinger equation, wave function, Airy beam