Bound State Wavefunctions vs Non-Bound State Wavefunctions

In summary, the difference between bound state wavefunctions and non-bound state wavefunctions lies in their graphical representations. Bound states can overlap or get close to each other, while non-bound states have WAVE FUNCTIONS at large distances that resemble scattering amplitudes. The bound state wave function can be seen as a pole for a replacement of K with iK in the scattering wave function, as there is no incoming wave in a bound state.
  • #1
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Bound vs "not"bound states

Homework Statement


Hi, I do not understand how two bound state wavefunctions differ from not bound state
wavefunctions.
To be more precise I m thinking about the graphical representation.

ons[/b2. Relevant equati

The Attempt at a Solution


I speculate that bound states can overlap or get close to each other.
Perhaps the problem is in meaning of "bound" in this particuular case?
Could someone help me to understand this better?
 
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  • #2


bound state wave functions are given by something like e(-kr)/r in comparison to non bound states for which WAVE FUNCTION at large distances are like Sle(ikr)/r+e(-ikr)/r where that Sl corresponds to scattering amplitude.You can see easily that bound state is just the pole for a replacement of K-->iK in scattering one because there is no incoming wave there.
 

FAQ: Bound State Wavefunctions vs Non-Bound State Wavefunctions

1. What is the difference between bound and not bound states?

Bound states refer to a state in which a particle is confined to a specific region or potential well, while not bound states refer to a state in which a particle is free to move without any confinement.

2. How can you determine if a state is bound or not bound?

A state is considered bound if the particle's energy is less than the potential barrier it is confined in. If the particle's energy is greater than the potential barrier, then it is considered not bound.

3. What are some examples of bound and not bound states?

An example of a bound state is an electron in an atom, as it is confined to the nucleus by the electrostatic attraction. An example of a not bound state is a free electron in a vacuum, as it has no confinement to a specific region.

4. How do bound and not bound states affect the behavior of particles?

Bound states result in the quantization of energy levels, whereas not bound states allow for continuous energy levels. This affects the behavior of particles, as bound states have discrete energy levels and not bound states have a continuous spectrum of energy.

5. Can a bound state become a not bound state?

Yes, a bound state can become a not bound state if the particle's energy increases to the point where it is greater than the potential barrier. This can happen through the absorption of energy or by increasing the potential barrier, such as in a chemical reaction or in a particle accelerator.

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