I think that the wave function is the description of a particle's position at a point in time. But I'm not precisely sure what an eigenfunction is and how it is different. I know that certain eigenfunctions return certain values, and that even if you do not have a certain eigenfunction you can consider it (the wave function?) to be the superposition of certain eigenfunctions. When you measure, however, the particle "collapses" to one of the composition functions. But what does this actually mean for the particle? Any help is appreciated!