Exercise14:

Chapter 6 problem 6.6: Wave packets Simlulation

Name:戴嘉禾

Number:2013301020073

Abstract

This paper investigated on collision of string wavepackets is done through numerical computation.The initial string profile is Gaussian .Both single and double Gaussian pluck are included.It shows that two such wavepackets pass through each other without changing shape or speed.The string signals versus time are also presented.It turns out that the signals are quite different at different position.And there are reasonable explanations for these signals.

Background discription

In classical physics, wave is wave and particle is particle. But in quantum mechanics, we are forced to admit that particle is also wave. But the free particle is certainly not monochromatic wave，because monochromatic waves cannot be normalized. Actually, a particle is refered as a wavepacket, with it's momentum being the average momentum of all the monochromatic waves who make up of the wavepacket. Now, we will analyse the propertis of a wavepacket.

Wavepackage diagram

figure.1 Sigle wave package

Analysis of Fig.1:

we get the moving configuration of a single wavepacket.The two components are unaffected by these collisions,that is,without changing shape or speed.And they reform the initial profile after an interval of time. Then we pick two points,one is a tenth from the left end,the other is the center.Here we show the string signal versus time of these two point.

For double case:

figure. 2 double wave packages

Analysis of Fig.2:

Angain,these wavepackets pass through each other without changing shape or speed and reform the initial profile after some time.

Link Code

Here is the code in my github

Acknowlegement and Reference

[1]: Cai Hao. https://github.com/caihao/computational_physics_whu.
[2]: Nicholas J.Giordano, Hisao Nakanishi.Computational physics.清华大学出版社
[3]:Thanks for student Shaosheng Yue and student Zhilin Wang.