Generating wavepackets in MATLAB

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!

Answer 1

[Youssef Khmou]

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.

[Sergio Manzetti]

Can this be done on ANY form of y, or is it only for that y in your example?

Say that I want to generate a wavepacket for cos(x) between 0 and 2pi, would it be similar to this, by replacing y by cos(x)?

[Youssef Khmou]

A wavepacket is a superposition of different harmonics and is localized in x or t, it can be generated using different functions, the real part of the provided example is the sum of cosine factors, you can generate other models of wavepacket such as gaussian function.

[Sergio Manzetti]

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]

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]

Thanks for this Youssef, this was indeed clear. I will try it out!