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Originally Posted by Qfwfq
I suppose you mean a potential well, which may be finite or infinite.
The standard way is to make the boundary conditions (simple in the more ideal case of infinite well, from R outward the amplitude is just plain zero). In both cases, with radial symmetry, the eigenstates are series of Bessel and Neuman functions but I can't remember details from years ago, exercises in basic theoretical physics course, but that's the most exact path.
Complicated, you might say. Perhaps the ground state energy can be estimated well enough, as you suggest. Heisenberg gives you the delta p and the particle whacking around inside the well can be modelled as a free particle between whacks. It's momentum p is therefore only changing in direction so delta p would be twice the modulus, apply E^2 - p^2 = m^2 and you should have a quite good estimate.
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Yea, the problem was for the girl I'm tutoring. It's a freshman year intro to modern physics type thing, so I imagine it must be the uncertainty estimate. I doubt they want you to solve explicitly and deal with the Bessel functions. Although, I suppose for the ground state you could set l=0, and then you've got a simple infinite potential well.
-Will
