# About scattering and bound states

• luisgml_2000
In summary, the conversation discusses the concepts of scattering, bound states, and antibound states in the context of scattering theory. A bound state has E < 0 and is confined to a compact region in space, while a scattering state is not confined and can leave any compact region given enough time. The conversation also provides some recommended reading materials for a deeper understanding of these concepts.
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!

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 don't say what your text is, which book do you use? Isn't these things defined somewhere?

Last edited by a moderator:
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.

## What is scattering?

Scattering is a phenomenon that occurs when particles, waves, or signals interact with each other in a way that alters their direction and/or intensity. It can occur in various physical systems, such as in atomic and nuclear physics, optics, and acoustics.

## How is scattering related to bound states?

Bound states are states of a system in which particles are confined to a specific region due to attractive forces. Scattering, on the other hand, involves particles moving freely and interacting with each other. However, bound states can be created through scattering processes, such as when particles interact and form a bound state after the interaction.

## What factors affect scattering?

The factors that affect scattering include the properties of the particles involved, such as their mass, charge, and spin, as well as the energy and angle of the incident particles. The type of interaction between the particles and the medium they are scattering through also plays a role.

## What is the difference between elastic and inelastic scattering?

Elastic scattering is a type of scattering in which the total energy of the particles remains the same before and after the interaction. Inelastic scattering, on the other hand, involves a transfer of energy between the particles, resulting in a change in their total energy.

## How is scattering used in research and practical applications?

Scattering is used in a variety of research fields, such as in particle physics, material science, and astrophysics, to study the properties and interactions of particles and materials. It also has practical applications, such as in medical imaging and security screening, where scattering techniques are used to detect and image objects and materials.

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