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**ARRGH! Particle Wavefunction Questions...**

Hello everyone at physicsforums.com!

Ook, I have a few questions, well, a lot actually. I guess I'll just ask two of them here. It is stated in quantum mechanics that a wave function (it's absolute square) tells the probability of finding a particle at a specific point, but what if one is dealing with an extended object, such as an atom or a basketball? Does the wavefunction tell us where we'll find the object's center of mass or what??

Now, if we have a point particle located at a specific point, then it's electric field is given as Cq/r^2, where r is the distance to that particle. But what if the particle is "smeared out in space"? I.e. the particle's wavefunction is an extended wavepacket rather than a delta function. Is the electric field the same in that case as the e. field of an extended charge distribution with charge density at each point proportional to the probability of finding the particle at that point? So, like, whould the e.field inside the wavepacket at some point be zero, increase as we move out of the wavepacket, and then start to decrease again? For example, when we solve the Shr. Equation for an atom, we assume that the nucleus is located at a specific point. But what if the nucleus is described as an extened wavepacket? When solving the Shr. Eq. for an electron bound to the nucleus,

*would our potential function (the one we substitute into the Shr. Eq) now be the same as the potential function of an extended charge distribution*?? Don't wavepackets spread out in time? So even if the nucleus was located at a specific point at some time, wouldn't it become an extended wavepacket later? So, like, the whole atom spreads out and the electron cloud gets deformed? But back to the charged particle described as a wavepacket. If we actually measure the electric field at a point "inside" the wavepacket, would we get a small value ( the same value we'd get if we measured the field inside a charge distribution) or would we get a large value (the same value as we'd get if the charge was concentrated at a specific point) and therefore localize the particle with our measurement?? Isn't that how we localize particles and collapse their wavefunctions anyway, by measuring the electric field?? But if we are using the Shr. Eq. to describe the motion of charged particle A in the vicinity of charged particle B (the latter is described by a wavepacket) would the potential function in the Shr. Eq.(the equation which we're solving for particle A, the potential is created by particle B) be just Cq/r^2 (which of course would also change in time since the position of particle B changes), or would the potential function in the Shr. eq. describing particle A be the same as that of an extended charge distribution with charge density at each point equal to the probability of finding particle B at that point, or would it be something else entirely??

P.S.

Sorry for such a long question (two or three questions actually, although it looks like a lot more), I've tried to make myself clear, don't know if I have though. Thanks to anyone who answers.