Does the wave function spread more quickly after it is observed?

[PeroK]

Of course, I could be wrong, I am human after all. The skeptical emoji is making me nervous...

The Internet is awash with simulations and lectures on the free particle wave-packet:

 

[Sciencemaster]

Honestly, I was hoping for an interactive simulation. I was hoping to create something like the first video, but then partway through collapse the wave function. Reflecting on this further, I can better say this as the collapse of the wave function creating a wider spread in the momentum space wave function through the Fourier Transform, which does indeed seem to happen, please correct me if I am wrong.

 

[atyy]

Honestly, I was hoping for an interactive simulation. I was hoping to create something like the first video, but then partway through collapse the wave function. Reflecting on this further, I can better say this as the collapse of the wave function creating a wider spread in the momentum space wave function through the Fourier Transform, which does indeed seem to happen, please correct me if I am wrong.

That's correct. A wave function with a narrow spread in position has a broad spread in momentum. That is the uncertainty principle. However, this does not say anything about how the spread changes with time.