Potential well

[Feynmanfan]

I'm confused when I study potential wells. I understand that when E<V0 there are eigenstates and only certain values of energy. I can express this condition with an equation and eigenfunctions.

However, if E>V0, it's not bounded and all values of energy are possible. This, I don't understand. It is true that the sprectrum can be discrete or continous but how would you explain this with a example, say the finite potential well.

Thanks.

[dextercioby]

The spectral problem admits solutions in any circumstances.It's just that some are nicer and require only Hilbert spaces and bounded operators and others rigged Hilbert spaces and unbounded operators.

This problem (of potential wells) is dealt with in a very mathematical way in the first volume of Galindo & Pascual:"Quantum Mechanics",Springer Verlag,1990.

Daniel.