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 equation 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 a 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, Schrodinger equation, wave function, Airy beam