How would one measure the position of a quantum mechanical particle? For example, suppose I am aware that an electron lies in a 1-D box of length L. And maybe I wish to know the position of the particle in that box to a certain level of accuracy. I'm satisfied with knowing the position within a range of L/2 for example. So I decide to divide the box into two seperate boxes somehow. (Note: The outer edges of the two boxes will have an infinte potential ensuring that there can be no quantum tunnelling.) Ok, so now i seperate my two boxes. One box is transported to Antarctica, and the other to Mexico. I think that quantum mechanics would suggest that a wavefunction is coexisting in both the boxes prior to any further measurements being made. Firstly, could someone please tell me if the above sentence is correct, because it seems very bizaar to me that a wavefunction of a particle can be discontinous, which would be required when the boxes are seperated. Now my final question is, what experiment might I be able to do in order to force the electron to collapse into one of the two boxes. Or another way of posing my question is, how can I determine which box the "particle" will lie in.