# About scattering and bound states

1. May 1, 2008

### luisgml_2000

Hi!

I'd like to ask you what do the texts mean by scattering, bound and antibound states. The context for these concepts is scattering theory.

Thanks!

2. May 2, 2008

### malawi_glenn

A bound state has E < 0

And scattering, well scattering is when you have a incident particle (wave function $\psi _{in}(x)$) which accected by a potential (scatterer $V(x)$) which leads to another (unbound) particle state (a new wave function [itex] \psi _{out}(x) [/itex).

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:

http://www3.tsl.uu.se/thep/courses/QM/scattering-overview.pdf (very good, with pictures and history)

http://farside.ph.utexas.edu/teaching/qmech/lectures/node130.html (sort of a textbook)

http://www.theorie.physik.uni-muenchen.de/~serge/scattering1.pdf (summary of formulas)

Its better to ask specific questions, if you want a good answer :-) This was a quite general question.

It is also quite hard to answer you since you dont say what your text is, which book do you use? Isn't these things defined somewhere?

3. May 2, 2008

### comote

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.