What's a firm/good definition of an "attractive" potential?

[Zacarias Nason]

What makes an attractive potential "attractive"? I've just started learning about 1D S.E.'s with delta potentials and see the phrase frequently but am having trouble discerning a good, clear definition of what that means.

 

[dextercioby]

It's a potential which allows the existence of bound states. If a potential allows only scattering states, it's called "repulsive".

 

[fresh_42]

Maybe these figures help a little to visualize it: