Understanding Scattering and Bound State Solutions in Quantum Mechanics

[Logan Rudd]

1)So from my understanding, as long as $E>0$ you will have scattering states and these scattering states will always result in an imaginary $\psi$, but bound states can also have an imaginary $\psi$? Is this correct and or is there a better way of looking at this maybe more conceptually?

2)I noticed in a footnote in griffiths intro to qm 2nd ed. in the finite square well section he mentions that he wrote $\psi$ in terms of sin/cos instead of exponentials because we know the solutions will be even or odd because the potential is symetric. But he also does it for the infinite square well when it's not really symmetric (at least with respect to the y-axis) and doesn't do it for the delta potential. How come he doesn't do it for the delta potential, is it not really symmetric? and why does he do it for the finite square well?
What is the benefit of "exploiting the even/odd solutions" and what does he mean by that?

Thanks

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?