# What is the criteria for bound states

• I
• ftr
In summary, the conversation discusses bound states and how they are defined as having energies that are specific and not general relations. The criteria for bound states is that they cannot have enough energy to fall apart. The binding energy is calculated from the total energy of the system. The uniqueness of binding energy is simply a result of its definition as an interaction energy that arises from solving Schrodinger's equation for a potential that vanishes at infinity.
ftr
I read this wiki and some of the references
https://en.wikipedia.org/wiki/Bound_state

But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.

Thanks

ftr said:
For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.
The specific energies of hydrogen are special cases.

What is unclear?

mfb said:
What is unclear?

What is the criteria for bound states?

They can't have enough energy to fall apart.

mfb said:
They can't have enough energy to fall apart.
Ok thanks. But I am still not clear, do you mean potential or kinetic, and how is the binding energy calculated from them.

edit: It also seems to be potential specific as in this paper
https://arxiv.org/pdf/hep-ph/0407258.pdf

I mean the total energy.

How to calculate the binding energy of a specific system depends on that system.

mfb said:
How to calculate the binding energy of a specific system depends on that system.

I guess my question is again what makes this binding energy unique as opposed to any other interaction energy that may arise.

ftr said:
I guess my question is again what makes this binding energy unique as opposed to any other interaction energy that may arise.
The only thing that's unique about it is that we've decided to call it "binding energy".

If you solve Schrodinger's equation for a potential that vanishes at infinity, you will find that some of the eigenstates vanish at infinity and some do not. We call the ones that do vanish at infinity "bound states", and we call their energy eigenvalues "binding energy".

## 1. What is a bound state in physics?

A bound state in physics is a state in which a particle or system is confined to a specific region of space due to the presence of a potential energy barrier. This means that the particle or system is unable to escape from this region and is therefore considered "bound". Examples of bound states include electrons in an atom or molecules in a chemical bond.

## 2. What is the criteria for a particle to be in a bound state?

The criteria for a particle to be in a bound state is that its total energy must be less than the potential energy barrier that it is confined to. This means that the particle's kinetic energy is not enough to overcome the potential energy barrier and escape from the bound region.

## 3. How do we determine if a system is in a bound state?

In order to determine if a system is in a bound state, we must first analyze the potential energy barrier that the system is confined to. We then calculate the total energy of the system and compare it to the potential energy barrier. If the total energy is less than the potential energy barrier, then the system is considered to be in a bound state.

## 4. Can a bound state exist in an infinite potential well?

Yes, a bound state can exist in an infinite potential well. In this case, the particle or system is confined to a finite region of space due to the infinite potential barriers at the edges of the well. The particle or system is still considered to be in a bound state as long as its total energy is less than the potential energy barrier.

## 5. What is the relationship between bound states and energy levels?

Bound states and energy levels are closely related. In a bound state, the energy of the particle or system is quantized, meaning it can only take on certain discrete values. These energy levels correspond to the potential energy barrier that the particle or system is confined to. As the energy levels increase, the particle or system is able to move further away from the potential energy barrier, but it is still considered to be in a bound state.

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