How do I plot a time-dependent probability density function on MATLAB?

[Elekko]

Homework Statement

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

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

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?

 

[Simon Bridge]

That's right - you pick a time that shows the important characteristics of the density function.
It's either that or create an animation.