原子链与弦中波包演化的比较分析

Comparative analysis of the moving of a wave packet in one-dimensional monatomic lattice with that in a string

分析了一维单原子链中与连续弦中的波包的演化过程.弦中的波包以恒定速度移动,且保持形状不变;而原子链中的波包在演化过程中形状不断地发生变化.通过比较分析一维单原子链与弦振动的色散关系,讨论了波包演化的不同以及离散的原子链到连续弦的过渡.

The moving of a wave packet in one-dimensional monatomic lattice and that in a string are analyzed. The profiles of the wave packet at different times are calculated and presented for both the systems. In onedimensional monatomic lattice, the profile of the wave packet is changing all the time. But in a string, the profile is unchanging and moving with a definite speed. The reason for the difference is that the two systems have different dispersion law. The dispersion law of the lattice vibration is nonlinear, whereas that of the string vibration is linear.