I am trying to develop a graphical, interactive simulation of a wave function in position space, given an arbitrary potential. It works great, but as a final touch, I would like the user to be able to collapse the wave function, either by measuring its position or its momentum. My problem is then, how do I calculate the momentum space wave function, given the position space wave function? I know that a simple Fourier transformation should do the job, but when I calculate it I always end up with some even momentum space wave function. Example: Make a 1D Gaussian wave packet in position space, travelling with speed v. Its momentum space wave function will also be Gaussian, centered on the origin. But it should be centered on v! How do you capture the information of movement from the position wave function alone, at a single instant? Thank you.