Yeah, I'm new here and saw a question that I actually knew something about. I didn't realize how old it was. Who knows, maybe someone will have a similar question 11 years from now and my response will help them out.
Normalizing is equivalent to being "bound". All being bound means is that you can find the particle within a definite region in space (even if that region is infinite like in the case of the single bound state for the Dirac potential). But remembering that the squared wavefunction gives the...
We know that in one dimension if ##E>V(\infty)## or ##E>V(-\infty)## then the resulting wave function will not be normalizable. The basic argument is that if ##E>V(\infty)##, then a stationary solution to the Schrodinger equation will necessarily have a concavity with the same sign as the...