why is the height for the particle in a box expressed in eV and not in meters?
Because it's an energy barrier instead of a wall.
so the original assumption was that the particle got blocked in a box by energy barriers?
Yes. It could be an electric potential for example.
I've seen a lot of people get confused by this. When you see a graph for the potential of a 1-d box, keep in mind that its a 1-d problem. The particle only has an x-coordinate. The height represented is the magnitude of the potential energy. Likewise, when you see a graph for the wavefunction of a particle in a 1-d box, don't thing of this as showing the hieght of the particle versus the horizontal displacement. The particle does not have a hieght: it is a 1-d problem! The hieght represents the value of the wavefunction at the given displacement. This hieght squared is proportional to the probability of the particle being found in a small region around the point.
thank you very much for clearing that up! :)
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