## Generating wavepackets in MATLAB

Sergio Manzetti

### Sergio Manzetti (view profile)

님이 질문을 제출함. 25 Jan 2018
최근 활동 Sergio Manzetti

### Sergio Manzetti (view profile)

님이 편집함. 31 Jan 2018
Youssef Khmou

### Youssef Khmou (view profile)

님이 답변을 채택함.
Hi, I am trying to generate wavepackets for a complex function using MATLAB, however, I am not sure on the approach. Does MATLAB Forum have a suggestion?
Thanks!

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### Youssef Khmou (view profile)

on 26 Jan 2018

Among the methods for generating wavepackets is linear superposition, considering the spatial dimension x, an elementary complex wavepacket can be generated as follows:
x=-20:0.005:20;
w=20;
dw=0.1;
y=exp(j*w*x)+exp(j*(w-dw)*x)+exp(j*(w+dw)*x);
plot(x,real(y));
the parameter dw is the frequency difference between the components, and has an impact on coherence length.

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Sergio Manzetti

### Sergio Manzetti (view profile)

on 30 Jan 2018
Thanks Youssef. One particular feature I was looking for was to find the wavepacket for the Schrödinger eqn. I have not found such an example on software tutorial etc.
Youssef Khmou

### Youssef Khmou (view profile)

on 31 Jan 2018
As an illustrative example, consider the 1D wavefunction of particle localized at x0=5 at t=0 with variables w and k:
x=0:0.01:10;
x0=5;
w=2;
k=2;
t=0;
the waveform can be generated by:
f=cos(k*(x-5)-w*t).*exp(-(k*(x-5)-w*t).^2);
for different values of t=1,2,..., you can compute the corresponding wavefunction.
Sergio Manzetti

### Sergio Manzetti (view profile)

on 31 Jan 2018
Thanks for this Youssef, this was indeed clear. I will try it out!

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