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## Main Question or Discussion Point

I have a question, and I'm positive it has a really simple answer, but I can't think of it right now.

In the infinite square well (the simplest bound problem), the wave functions have discrete energy values. We can have a wave function that's a linear superposition of any number of these so that the

So, let's say we have an electron moving in 0 potential with a well defined momentum p. This means it has a well defined energy [itex]E = p^2/2m[/itex], and let's say this E isn't one of the discrete energy levels of the infinite square well we're looking at. Now let's say and it gets captured in this infinite square well. It could have the same

So what happens? Can it not be captured? If it is, does it form some new wave function with the average energy equal to the initial one? This would seem sketchy to me, because there are obviously an infinite number of combos that could give that average energy.

Thanks!

In the infinite square well (the simplest bound problem), the wave functions have discrete energy values. We can have a wave function that's a linear superposition of any number of these so that the

*average*value of the energy we measure is any value (above the ground state energy, of course), but at the end of the day each measurement will yield one of the discrete energy values allowed.So, let's say we have an electron moving in 0 potential with a well defined momentum p. This means it has a well defined energy [itex]E = p^2/2m[/itex], and let's say this E isn't one of the discrete energy levels of the infinite square well we're looking at. Now let's say and it gets captured in this infinite square well. It could have the same

*average*energy that it had before capture, but necessarily some measurements would yield a higher energy than its initial energy, if you constructed some wave function that had the average energy equal to its initial (pre-capture) energy.So what happens? Can it not be captured? If it is, does it form some new wave function with the average energy equal to the initial one? This would seem sketchy to me, because there are obviously an infinite number of combos that could give that average energy.

Thanks!