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## Homework Statement

Given that, in free space the probability density for a wave function (free particle) is [tex]\mid \Psi(x,t)\mid^2=P(x,t)=\frac{\sigma_0}{\mid \alpha \mid^2\sqrt{\pi}}exp(-(\frac{\sigma_0}{\mid \alpha \mid})^4\frac{(x-x_0-p_0t/m)^2}{\sigma_0^2})[/tex]

What is need to be done is to study a wave packet of size [tex]\sigma_0=\frac{L}{10}[/tex] at [tex]x_0=0[/tex] on the interval [tex]-L/2\leq x \leq L/2[/tex]

I need to plot this probability density function on MATLAB.

Since this PDF is time dependent I actually don't know how I should plot it? I know the interval should go between -L/2 and L/2 but how should this depend on time?

## The Attempt at a Solution

Should I just create a vector from -L/2 to L/2 and then just have an arbitrary time?

Basically I cannot "visualize" in mind how it should look like before plotting, as I don't know how it exactly has to be done?