Propagation and spreading of a pulse or wave packet
Propagation and spreading of a pulse or wave packet
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脉冲或波包的传播和扩展
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
H. M. Bradford
中科院分区：
文献类型：
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作者：
H. M. Bradford
通常教科书上关于波包速度和传播的讨论都是基于特殊情况和近似，其有效性范围有限。本文通过考虑波包矩的时间依赖性，得到了更一般的关系式。真实的正弦平面波的包（真实的脉冲，例如，声音）和复指数平面波包（例如，自由粒子的量子力学波函数）。如果真实的波包不包含驻波分量，则结果相似。结果表明，波包的质心以群速度的加权平均的等速运动。波包的扩展取决于群速度的方差与最小波包宽度前后时间间隔的平方的乘积。数据包像自由飞行的粒子集合一样移动和扩散，其中粒子的速度是...
The usual textbook discussions of the velocity and spreading of a wave packet are based on special cases and approximations which have a limited range of validity. In this paper more general relations are obtained by considering the time dependence of the moments of a wave packet. Both a packet of real sinusoidal plane waves (a real pulse, e.g., sound) and a packet of complex exponential plane waves (e.g., the quantum‐mechanical wave function of a free particle) are considered. The results are similar if the real wave packet contains no standing wave components. It is shown that the centroid of a wave packet moves at a constant velocity which is a weighted average of the group velocity. The spreading of the wave packet depends on the product of the variance of the group velocity and the square of the time interval before or after the time of minimum packet width. The packet moves and spreads like a collection of particles in free flight, in which the velocities of the particles are the group velocities of...