QM: Finite square well with V>0

Homework Statement

Hi all.

When talking about the finite square well with a potential V > 0 for - A < x < A, I have never seen an example of bound states (i.e. E<0). They only treat examles with scattering states (i.e. E>0). Is there any reason for this? My book (Griffith's Intro. to QM) does not talk about this scenario.

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If V>0, then this is not a square well, but a square barrier. Bound states do not exist in this situation.

Ahh yes, barrier - not well! Why is that?

A well is when V<0, so the particle can "fall in". A barrier is V>0, so there's an obstacle. I'm not sure about a formal proof, but it is hard to imagine a particle bound to a wall. Total energy must be negative somewhere if there is to be a bound state, but kinetic energy is always positive, plus positive potential = no bound state.

Can one use the explanation that the energy E always has to be larger than the minimum potential?