Generating wavepackets in MATLAB

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Sergio Manzetti
Sergio Manzetti 2018-1-25
编辑： Sergio Manzetti 2018-1-31
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
Youssef Khmou 2018-1-26
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
Youssef Khmou 2018-1-31
编辑：Youssef Khmou 2018-1-31
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 2018-1-31
编辑：Sergio Manzetti 2018-1-31
Thanks for this Youssef, this was indeed clear. I will try it out!

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