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I can picture a bound state in a harmonic oscillator, or in an infinite square well, but where is a particle bound in a delta potential?

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This is a good question because it seems like you can only measure the particle with negative kinetic energy. That is, the spatial part where the particle is in the well has width zero. –  santa claus Mar 17 '13 at 19:40

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Where a particle is, in my opinion, it's not a very good to question to ask in the context of quantum mechanics. You can solve the delta problem and then compute the probability density for the particle. That will give you information of where may the particle be if you try to measure its position. But before doing that, it does not make too much to ask where the particle is.

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See my comment above. It sort of does make sense to ask this, because the probability that you measure the particle in the well itself is vanishingly small. So it seems you can only "measure" the particle with negative kinetic energy (though I'm sure the measurement itself would kick the electron out of the bound state -- perhaps you can elaborate on this.) –  santa claus Mar 17 '13 at 19:42
    
I'm sorry but I can't actually say anything about how to do the actual measurement, but it is indeed a very good thought, you should consider posting it as a question. –  Jorge Mar 17 '13 at 20:34

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