一般波包在均匀场中的运动

General wave packets in a homogeneous field

求出了一般波包的中心和宽度在一维均匀场中的变化规律 .波包的中心遵循经典粒子的运动规律 ,宽度的平方则以时间的二次函数增长 .但动量空间的相应波包却保持其宽度不变 ,特别是平面波在运动过程中仍保持为平面波 .对Gauss波包 ,求出了波函数随时间变化的显式 ,验证了一般结论 .

The centroid and width of a general wave packet moving in a homogeneous field in one dimension are obtained as explicit functions of time.The centroid moves like a classical particle,and the width increases with time quadratically.However,the width of the corresponding wave packet in the momentum space does not vary with time,so a plane wave remains to be a plane wave at any time.The time dependence of a Gaussian wave packet is worked out explicitly and the general results are verified.