I'm wondering how the wave functions of two particles would evolve through time if they cross paths. Say you have an electron whose wave functon comes close to another charged particle, like an alpha particle. Now I believe if the alpha particle is well localised you can treat it has a point charge and use the time independant schrodinger equation to determine how the electrons wave function changes through time. But what if the alpha particle is not well localised and its wavefunction is spread out? How will the electrons wave function evolve? Is there anyway to give me an idea without going into too much detail? btw im guessing since the alpha particle is so heavy it wont be affected much by an electron moving at a moderate speed.