Bound State Wavefunctions vs Non-Bound State Wavefunctions

[prehisto]

Bound vs "not"bound states

Homework Statement

Hi, I do not understand how two bound state wavefunctions differ from not bound state
wavefunctions.
To be more precise I m thinking about the graphical representation.

ons[/b2. Relevant equati

The Attempt at a Solution

I speculate that bound states can overlap or get close to each other.
Perhaps the problem is in meaning of "bound" in this particuular case?
Could someone help me to understand this better?

 

[andrien]

bound state wave functions are given by something like e^(-kr)/r in comparison to non bound states for which WAVE FUNCTION at large distances are like S_le(ikr)/r+e(-ikr)/r where that S_l corresponds to scattering amplitude.You can see easily that bound state is just the pole for a replacement of K-->iK in scattering one because there is no incoming wave there.