So I know that I've been asking alot of quantum questions lately, but I'm taking the course this year, and questions keep looming:
With respect to the schrodinger equation, I've been told that when E>0 you encounter a scattering state, and when E<0 you encounter a bound state. The question I have is qualitatively determining whether the energy is greater or less than 0.
For instance, if we have a 1-D finite square well, where V(x), the potential, equals -Vo between -a and a (centered around x = 0), and otherwise the potential equals 0 (as x-> +/- infinity), how can one instantly tell if bound states or scattering states are going to occur. The real point is being able to look at a situation, and know if the energy will be less than or greater than the potential (which is general 0 at +/- infinity)
Thanks a bunch.