The Wave packet: Moving as a quantum particle

郭帅斐

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The introduction:

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.

The pseudo-code：

As a one-dimentional Wave Propagation，we differencing the equation and get the numerical equation:

$$y(i,n+1)=2*(1-r^2)*y(i,n)-y(i,n-1)+r^2*[y(i+1,n)+y(i-1,n)]$$
where the $r=\frac{c\Delta t}{\Delta x}$ is the papameter.

The result:

• After runing the simple program,we get the moving configuration of a single wavepacket. The figure is showen as follows:
  
  We see clearly the moving and reflect of the wavepacket!
• After running another problem
  We find that two wavepacket moving independantly.The figure is shown as follows:
  
• We also find that the wave transmits from one mediator to another. The figure is as follows:
  

The conclusion:

With a differenced wave equation, we see the moving of a wavepacket including: runing independantly,reflect and transmit.