Propagation Nature Research on Quantum Mechanics Wave Packet in Several Kinds of Common Potential Fields

In this paper,the propagation nature of the wave packet was discussed through the Green's function under three common potential fields.We had discovered some valuable conclusions.Firstly,when the wave packet of free particle varied with the time,the wave packet center of gravity moved by a speed 0/μ, but when the wave packet amplitude changed from the initial δ to the final δt,the Position variable r still deferred to the Gaussian distribution. Secondly,the wave packet amplitude in a homogeneous field changed by a power series with relative to the initial time.Finally,in simple harmonics oscillator potential field,the momentum mean value in random time is precisely the momentum form of classical simple harmonics oscillator.