Scattered states and bound states ?

In summary, the topic is about the effective pair potential in hydrogenic systems and how it is defined by the two-particle radial distribution function. The rdf is a sum of contributions from scattered states and bound states, which are influenced by a scattering potential and have different characteristics. While a bound state is localized and normalized, a scattered state is not. This can be confusing as bound states often have an exponential wave function, but the important distinction is that a bound state approaches zero at infinity while a scattered state has a nontrivial value.
  • #1
hiphys
3
0
Hello,I'm physics student.I'm from Vietnam and my English is not very good.
I was wondering if anyone could help me out with a question : what are scattered states and bound states ?
I'm interested in "Temperature-dependent Coulomb interation in hydrogenic systems".
In this topic,the effective pair potential is defined as afunction of the two-particle radial distribution function (rdf).
When particles have charges of opposite sign,their rdf can be considered as a sum of two terms : the contributions from scattered states and bound states .
I 've looked up those in many books,but I haven't found the answer.Please help me.Thanks.
 
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  • #2
I don't know what the topic means by that, but a scattered state is one that is influenced by a scattering potential but has nontrivial |ψ|2 at r -> infinity, and a bound state is one that has |ψ|2 -> 0 at r -> infinity.
 
  • #3
turin said:
I don't know what the topic means by that, but a scattered state is one that is influenced by a scattering potential but has nontrivial |ψ|2 at r -> infinity, and a bound state is one that has |ψ|2 -> 0 at r -> infinity.
I s this means that the bound state is localized and normalized, and the scattered state is not?if so why is that as I think it is the opposite as the bound state usually given by exponential function and ,e.g bound particle always have an exponential wave function?so this means is not narmalised, please show me where is my confusion
 

What are scattered states and bound states?

Scattered states and bound states are two types of states that describe the motion and behavior of particles in a system. Scattered states refer to particles that are free to move and are not confined to a specific region, while bound states refer to particles that are confined to a specific region and have a stable energy level.

What is the difference between scattered states and bound states?

The main difference between scattered states and bound states is the confinement of particles. In scattered states, particles are free to move and are not confined to a specific region, while in bound states, particles are confined to a specific region and have a stable energy level.

How are scattered states and bound states related?

Scattered states and bound states are related in the sense that they both describe the motion and behavior of particles in a system. In some systems, particles may transition between scattered states and bound states depending on external factors such as temperature or pressure.

What are some examples of systems with scattered states and bound states?

Scattered states and bound states can be found in various systems, including atoms, molecules, and solids. In atoms, electrons can occupy both scattered states and bound states, while in molecules, the motion of the nuclei can be described by both scattered states and bound states. In solids, the motion of electrons can be described by both types of states as well.

Why is the study of scattered states and bound states important?

The study of scattered states and bound states is important because it helps us understand the behavior of particles in different systems. This knowledge is crucial in various fields such as physics, chemistry, and materials science, and can help us develop new technologies and improve our understanding of the natural world.

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