# Generating wavepackets in MATLAB

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Sergio Manzetti le 25 Jan 2018
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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### Réponse acceptée

Youssef Khmou le 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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Youssef Khmou le 31 Jan 2018
Modifié(e) : Youssef Khmou le 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 le 31 Jan 2018
Modifié(e) : Sergio Manzetti le 31 Jan 2018
Thanks for this Youssef, this was indeed clear. I will try it out!

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