And scattering, well scattering is when you have a incident particle (wave function [itex]\psi _{in}(x)[/itex]) which accected by a potential (scatterer [itex]V(x)[/itex]) which leads to another (unbound) particle state (a new wave function [itex]\psi _{out}(x) [/itex).<br />
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That is perhaps the most simple explanation I can give, I am sure you will understand more later. Here are some good introductory material I used when I started with Quantum scattering:<br />
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http://www3.tsl.uu.se/thep/courses/QM/scattering-overview.pdf (very good, with pictures and history)<br />
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<a href="http://farside.ph.utexas.edu/teaching/qmech/lectures/node130.html" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://farside.ph.utexas.edu/teaching/qmech/lectures/node130.html</a> (sort of a textbook)<br />
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http://www.theorie.physik.uni-muenchen.de/~serge/scattering1.pdf (summary of formulas)<br />
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Its better to ask specific questions, if you want a good answer :-) This was a quite general question.<br />
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It is also quite hard to answer you since you don't say what your text is, which book do you use? Isn't these things defined somewhere?[/itex]
I claim ignorance about anti-bound states.
A good reference about bound states and scattering states is D Ruelle "A remark on bound states in Potential Scattering theory" Nouvo Cimento V61A p655-662. It is a bit heavy on the math though.
The basic idea they give is that a bound state is any state which is "confined" to a compact region in space for all time. In contrast a scattering state will leave any compact region of space given enough time.
This makes sense if you think about it. A Bound state is "BOUND" to some finite region for all time where as a scattering state is not.